{
 "cells": [
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   "source": [
    "# Lecture 15 - Advanced Curve Fitting: Gaussian Process Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set_context('talk')\n",
    "sns.set_style('white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectives\n",
    "\n",
    "+ To do regression using a GP.\n",
    "+ To introduce some diagnostics for how good a probabilistic regression is.\n",
    "+ To find the hyperparameters of the GP by maximizing the (marginal) likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Readings\n",
    "\n",
    "+ Please read [this](http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/pdfs/pdf2903.pdf) OR watch [this video lecture](http://videolectures.net/mlss03_rasmussen_gp/?q=MLSS).\n",
    "\n",
    "+ [Chapter 3 from C.E. Rasmussen's textbook on Gaussian processes](http://www.gaussianprocess.org/gpml/chapters/RW2.pdf)\n",
    "\n",
    "+ [Section 5.4 in GP for ML textbook](http://www.gaussianprocess.org/gpml/chapters/RW5.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivation: A fully Bayesian paradigm for curve fitting\n",
    "\n",
    "Remember why we are doing this:\n",
    "\n",
    "+ Let's say that you have to learn some function $f(\\cdot)$ from some space $\\mathcal{X}$ to $\\mathbb{R}$ (this could either be a supervised learning problem (regression or classification) or even an unsupervised learning problem.\n",
    "\n",
    "+ You sit down and you think about $f(\\cdot)$. What do you know about it? How large do you expect it be? How small do you expect it be? Is it continuous? Is it differentiable? Is it periodic? How fast does it change as you change its inputs?\n",
    "\n",
    "+ You create a probability measure on the space of functions in which $f(\\cdot)$ lives which is compatible with everything you know about it. Abusing mathematical notation a lot, let's write this probability measure as $p(f(\\cdot))$. Now you can sample from it. Any sample you take is compatible with your prior beliefs. You cannot tell which one is better than any other. Any of them could be the true $f(\\cdot)$.\n",
    "\n",
    "+ Then, you get a little bit of data, say $\\mathcal{D}$. You model the likelihood of the data, $p(\\mathcal{D}|f(\\cdot))$, i.e., you model how the data may have been generated if you knew $f(\\cdot)$.\n",
    "\n",
    "+ Finally, you use Bayes' rule to come up with your posterior probability measure over the space of functions:\n",
    "$$\n",
    "p(f(\\cdot)|\\mathcal{D}) \\propto p(\\mathcal{D}|f(\\cdot)) p(f(\\cdot)),\n",
    "$$\n",
    "which is simultaneously compatible with your prior beliefs and the data.\n",
    "\n",
    "In the last lecture, we formalized mathematically the prior $p(f(\\cdot))$.\n",
    "Today, we will mathematically formalize the posterior $p(f(\\cdot)|\\mathcal{D})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reminder: The prior $p(f(\\cdot))$\n",
    "\n",
    "In the previous lecture, we defined $p(f(\\cdot))$ through the concept of a Gaussian process (GP), a generalization of a multivariate Gaussian distribution to\n",
    "*infinite* dimensions.\n",
    "We argued that it defines a probability measure on a function space.\n",
    "We wrote:\n",
    "$$\n",
    "f(\\cdot) \\sim \\mbox{GP}\\left(m(\\cdot), k(\\cdot, \\cdot) \\right),\n",
    "$$\n",
    "where \n",
    "$m:\\mathbb{R}^d \\rightarrow \\mathbb{R}$ is the *mean function* and \n",
    "$k:\\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}$ is the *covariance function*.\n",
    "\n",
    "We also discuss in detail the meaning of these equations.\n",
    "Namely that for any points $\\mathbf{x}_{1:n}=(\\mathbf{x}_1,\\dots,\\mathbf{x}_n)$, the joint probability density of the function values:\n",
    "$$\n",
    "\\mathbf{f}_{1:n} =\n",
    "\\left(\n",
    "f(\\mathbf{x}_1),\n",
    "\\dots,\n",
    "f(\\mathbf{x}_n)\n",
    "\\right).\n",
    "$$\n",
    "is the multivariate Gaussian:\n",
    "$$\n",
    "\\mathbf{f}_{1:n} | \\mathbf{x}_{1:n} \\sim \\mathcal{N}\\left(\\mathbf{m}(\\mathbf{x}_{1:n}), \\mathbf{K}(\\mathbf{x}_{1:n}, \\mathbf{x}_{1:n}) \\right),\n",
    "$$\n",
    "with mean vector:\n",
    "$$\n",
    "\\mathbf{m}(\\mathbf{x}_{1:n}) =\n",
    "\\left(\n",
    "m(\\mathbf{x}_1),\n",
    "\\dots,\n",
    "m(\\mathbf{x}_n)\n",
    "\\right),\n",
    "$$\n",
    "and covariance matrix:\n",
    "$$\n",
    "\\mathbf{K}(\\mathbf{x}_{1:n}, \\mathbf{x}_{1:n}) = \\left(\n",
    "\\begin{array}{ccc}\n",
    "k(\\mathbf{x}_1,\\mathbf{x}_1) & \\dots & k(\\mathbf{x}_1, \\mathbf{x}_n)\\\\\n",
    "\\vdots & \\ddots & \\vdots\\\\\n",
    "k(\\mathbf{x}_n, \\mathbf{x}_1) & \\dots & k(\\mathbf{x}_n, \\mathbf{x}_n)\n",
    "\\end{array}\n",
    "\\right).\n",
    "$$\n",
    "Please note that all the above expressions are conditional on the hyperparameters of the covariance function, e.g., lengthscales and signal variance for the squared exponential.\n",
    "However, for now, we do not explicitly show this dependence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian process regression\n",
    "\n",
    "Assume that the data we observe is:\n",
    "$$\n",
    "\\mathcal{D} = (\\mathbf{x}_{1:n}, y_{1:n}),\n",
    "$$\n",
    "where $y_i$ is not exactly $f(\\mathbf{x}_i)$, but it may have some noise.\n",
    "For the sake of simplicity, let's assume that the noise is Gaussian with variance $\\sigma$ (you can relax this, but things will no longer be analytically available).\n",
    "Assume that $\\sigma$ is known (for now).\n",
    "So, we have:\n",
    "$$\n",
    "y_i|f(\\mathbf{x}_i) \\sim \\mathcal{N}(f(\\mathbf{x}_i), \\sigma^2),\n",
    "$$\n",
    "for a single observation.\n",
    "For all the observations together, we can write:\n",
    "$$\n",
    "y_{1:n}| \\mathbf{f}_{1:n} \\sim \\mathcal{N}(\\mathbf{f}_{1:n}, \\sigma^2\\mathbf{I}_n),\n",
    "$$\n",
    "where $\\mathbf{I}_n$ is the $n\\times n$ unit matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's draw a graphical model representation what we have here.\n",
    "Remember that $\\sigma$ and the hyperparameters of the covariance function, let's call them $\\theta$, are (for the time being) fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "execution_count": 2,
     "metadata": {},
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    }
   ],
   "source": [
    "from graphviz import Digraph\n",
    "g = Digraph('gp')\n",
    "g.node('sigma', label='<&sigma;>', style='filled')\n",
    "g.node('theta', label='<&theta;>', style='filled')\n",
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    "g.node('y1n', label='<<b>y</b><sub>1:n</sub>>', style='filled')\n",
    "g.edge('theta', 'f')\n",
    "g.edge('x1n', 'f')\n",
    "g.edge('f', 'y1n')\n",
    "g.edge('sigma', 'y1n')\n",
    "g.render('gp_reg1', format='png')\n",
    "g"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, far so good, but how do we make predictions?\n",
    "How do we get $p(f(\\cdot)|\\mathcal{D})$.\n",
    "There are some nuances here.\n",
    "We are looking for a posterior measure over a function space.\n",
    "This is a strange beast.\n",
    "The only way we can describe it is through the joint probability density of the function values at any arbitrary collection of **test** points.\n",
    "So, let's take $n^*$ such test points:\n",
    "$$\n",
    "\\mathbf{x}^*_{1:n^*} = \\left(\\mathbf{x}^*_1,\\dots,\\mathbf{x}^*_{n^*}\\right).\n",
    "$$\n",
    "Imagine that these cover the input space as densely as we wish.\n",
    "Consider the vector of function values at these test points:\n",
    "$$\n",
    "\\mathbf{f}^*_{1:n^*} = \\left(f(\\mathbf{x}_1^*),\\dots,f(\\mathbf{x}^*_{n^*})\\right).\n",
    "$$\n",
    "We will derive the posterior over these points, i.e., we will derive $p(\\mathbf{f}^*|\\mathcal{D})$.\n",
    "And we will be happy with that.\n",
    "\n",
    "From the definition of the GP, we can now write the joint probability density of $\\mathbf{f}$ and $\\mathbf{f}^*$.\n",
    "It is just a multivariate Gaussian.\n",
    "We have:\n",
    "$$\n",
    "p(\\mathbf{f}_{1:n}, \\mathbf{f}^*_{1:n^*} | \\mathbf{x}_{1:n}, \\mathbf{x}^*_{1:n^*}) = \\mathcal{N}\\left(\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "\\mathbf{f}_{1:n}\\\\\n",
    "\\mathbf{f}^*_{1:n^*}\n",
    "\\end{array}\n",
    "\\right)\\middle |\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "\\mathbf{m}(\\mathbf{x}_{1:n})\\\\\n",
    "\\mathbf{m}(\\mathbf{x}^*_{1:n^*})\n",
    "\\end{array}\n",
    "\\right),\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "\\mathbf{K}(\\mathbf{x}_{1:n}, \\mathbf{x}_{1:n}) & \\mathbf{K}(\\mathbf{x}_{1:n}, \\mathbf{x}^*_{1:n^*})\\\\\n",
    "\\mathbf{K}(\\mathbf{x}^*_{1:n^*}, \\mathbf{x}_{1:n}) & \\mathbf{K}(\\mathbf{x}^*_{1:n^*}, \\mathbf{x}_{1:n^*})\n",
    "\\end{array}\n",
    "\\right)\n",
    "\\right),\n",
    "$$\n",
    "where the block matrix is just the covariance matrix of all inputs $\\mathbf{x}_{1:n}$ (observed) and $\\mathbf{x}^*_{1:n^*}$ (test).\n",
    "Let's visualize the situation again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "<text text-anchor=\"start\" x=\"191.5\" y=\"-159.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">*</text>\n",
       "<text text-anchor=\"start\" x=\"199.5\" y=\"-159.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">1:n*</text>\n",
       "</g>\n",
       "<!-- xs1ns&#45;&gt;f -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>xs1ns&#45;&gt;f</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M184.8582,-146.3771C174.3605,-136.8096 160.7214,-124.379 148.9225,-113.6255\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"151.2347,-110.9974 141.4861,-106.8481 146.5195,-116.171 151.2347,-110.9974\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1a25c94f50>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g2 = Digraph('gp2')\n",
    "g2.node('sigma', label='<&sigma;>', style='filled')\n",
    "g2.node('theta', label='<&theta;>', style='filled')\n",
    "g2.node('x1n', label='<<b>x</b><sub>1:n</sub>>', style='filled')\n",
    "g2.node('f', label='<<b>f</b><sub>1:n</sub>, <b>f</b>*<sub>1:n*</sub>>')\n",
    "g2.node('y1n', label='<<b>y</b><sub>1:n</sub>>', style='filled')\n",
    "g2.node('xs1ns', label='<<b>x</b>*<sub>1:n*</sub>>', style='filled')\n",
    "g2.edge('theta', 'f')\n",
    "g2.edge('x1n', 'f')\n",
    "g2.edge('f', 'y1n')\n",
    "g2.edge('xs1ns', 'f')\n",
    "g2.edge('sigma', 'y1n')\n",
    "g2.render('gp_reg2', format='png')\n",
    "g2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, now we have only finite dimensional probability densities.\n",
    "This is great. We know what to do next.\n",
    "We will use the basic probability rules:\n",
    "$$\n",
    "\\begin{array}{ccc}\n",
    "p(\\mathbf{f}^*_{1:n^*} | \\mathbf{x}^*_{1:n^*}, \\mathcal{D}) &=& p(\\mathbf{f}^*_{1:n^*} | \\mathbf{x}^*_{1:^*}, \\mathbf{x}_{1:n}, \\mathbf{y}_{1:n})\\\\\n",
    "&=& \\int p(\\mathbf{f}_{1:n}, \\mathbf{f}^*_{1:n^*} | \\mathbf{x}^*_{1:^*}, \\mathbf{x}_{1:n}, \\mathbf{y}_{1:n})d\\mathbf{f}_{1:n}\\;\\text{(sum rule)}\\\\\n",
    "&\\propto& \\int p(\\mathbf{y}_{1:n}| \\mathbf{f}_{1:n}) p(\\mathbf{f}_{1:n}, \\mathbf{f}^*_{1:n^*}|\\mathbf{x}^*_{1:^*}, \\mathbf{x}_{1:n}) d\\mathbf{f}_{1:n}\\;\\text{(Bayes' rule)}.\n",
    "\\end{array}\n",
    "$$\n",
    "This is the integral of a Gaussian times a Gaussian.\n",
    "We are not going to go into the details, but you can actually do it analytically.\n",
    "The result is... a Gaussian:\n",
    "$$\n",
    "p(\\mathbf{f}^*_{1:n^*}| \\mathbf{x}^*_{1:n^*}, \\mathcal{D}) = \\mathcal{N}\\left(\\mathbf{f}^*_{1:n^*}\\middle| \\mathbf{m}_n(\\mathbf{x}^*_{1:n^*}), \\mathbf{K}_n(\\mathbf{x}^*_{1:n^*},\\mathbf{x}^*_{1:n^*})\\right),\n",
    "$$\n",
    "where *posterior mean function* is:\n",
    "$$\n",
    "m_n(x) = m(x) + \\mathbf{k}(x,\\mathbf{x}_{1:n})\\left(\\mathbf{K}(\\mathbf{x}_{1:n},\\mathbf{x}_{1:n})+\\sigma^2I_n\\right)^{-1}\\left(\\mathbf{y}_{1:n} - \\mathbf{m}(\\mathbf{x}_{1:n})\\right),\n",
    "$$\n",
    "and the *posterior covariance function* is:\n",
    "$$\n",
    "k_n(x, x') = k(x,x') - \\mathbf{k}(x,\\mathbf{x}_{1:n})\\left(\\mathbf{K}(\\mathbf{x}_{1:n},\\mathbf{x}_{1:n})+\\sigma^2I_n\\right)^{-1}\\mathbf{k}^T(x,\\mathbf{x}_{1:n}),\n",
    "$$\n",
    "with\n",
    "$$\n",
    "\\mathbf{k}(x,\\mathbf{x}_{1:n}) = \\left(k(x,\\mathbf{x}_1),\\dots,k(x,\\mathbf{x}_n)\\right)\n",
    "$$\n",
    "being the cross-covariance vector.\n",
    "\n",
    "Now notice that the test points $\\mathbf{x}^*_{1:n^*}$ are arbitrary and that the joint distribution of the function values at these points, $\\mathbf{f}^*$, conditioned on the observations $\\mathcal{D}$ is a multivariate Gaussian with a mean and covariance matrix specified by the posterior mean and covariance functions, respectively.\n",
    "This is the defintion of a Gaussian process!\n",
    "Therefore, we conclude that the posterior probability measure over the space of functions is also a Gaussian process:\n",
    "$$\n",
    "f(\\cdot)|\\mathcal{D} \\sim \\operatorname{GP}(m_n(\\cdot), k_n(\\cdot, \\cdot)).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The point predictive distribution\n",
    "\n",
    "What if you just want to make a prediction at a single point?\n",
    "How do you do that?\n",
    "Well, this is quite simple.\n",
    "Your \"test points\" $\\mathbf{x}^*_{1:n^*}$ are now just a single point, say $\\mathbf{x}^*$.\n",
    "Your prediction about the function value at this point is captured by:\n",
    "$$\n",
    "p\\left(f(\\mathbf{x}^*) | \\mathcal{D}\\right) = \\mathcal{N}\\left(f(\\mathbf{x}^*)\\middle|m_n(\\mathbf{x}^*), \\sigma_n^2(\\mathbf{x}^*)\\right),\n",
    "$$\n",
    "where the *predictive variance* is just:\n",
    "$$\n",
    "\\sigma_n^2(\\mathbf{x}^*) = k_n(\\mathbf{x}^*,\\mathbf{x}^*).\n",
    "$$\n",
    "This is what we will be using the most.\n",
    "\n",
    "Now, if you wanted to predict $y^*$ at $\\mathbf{x}^*$, i.e., the measurement at $\\mathbf{x}^*$, you have do this:\n",
    "$$\n",
    "p(y^*|\\mathbf{x}^*, \\mathcal{D}) = \\int p(y^*|f(\\mathbf{x}^*)) p(f(\\mathbf{x}^*)|\\mathcal{D}) df(\\mathbf{x}^*) = \\mathcal{N}\\left(f(\\mathbf{x}^*)\\middle|m_n(\\mathbf{x}^*), \\sigma_n^2(\\mathbf{x}^*)+\\sigma^2\\right).\n",
    "$$\n",
    "Notice that you need to add the noise variance when you are talking about the measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Gaussian process regression in 1D with fixed hyper-parameters\n",
    "\n",
    "Let's generate some synthetic 1D data to work with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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79u09Y2VlZSooKFBBQYHKyso8x5OTk9W7d28VFBQoOzvbs9n5woULmj17to4fP67bb79dPXv2bLgLBAAA9RKSb4OPiopSVlaWJk2apMzMTK1cuVIJCQnavn27Tp48qRtuuEFPP/10la85ceKEhg8fLqmiq3NCQoJnbO7cuRozZoxeeeUVrVu3Tj169NCePXt0+PBhxcfH67nnnmvQ6wMAAPUTkitAkpSSkqLly5frzjvv1LFjx5SXl6crr7xSjz32mJYuXao2bdr4PFePHj307rvvKj09XT/++KPWr18vSXrooYf0zjvvXLZJYmPwd5c/TwUAAIwoJFeA3BITEzV//nyfzk1ISFB+fv5lx+Pj4zV37txAlRYUVqtVNpvN57cAu/tJZGRksEEOAGAoIbsCZDQOh0M2m02Sb02vKjfTstlsrAQBAAyFABQiTCaTz50/vXUS5SkBAICREIBCiC/tz31pow4AQKgjAIWYmkIQ4QcAgAohvQnaqNyhxh12LBaL5s2bp+LiYs85hB8AgJGxAhSiqq8EEX4AAPgnAlAIM5vNio2NrXIsNjaW8AMAMDwCUAiz2+1VVn6kipWg2h6RBwAg1BGAQlT1Dc+VV4J86RMEAEAoIwCFIG9PexUVFfncJwgAgFBHAAoxNT3q7kufIAAAjIAAFEJ86fNDCAIAgAAUMhwOh89NDr2FIN4FBgAwEgJQiDCZTMrIyJDkW5+fyiEoIyODd4EBAAyFTtAhxGq1aujQoT6HGbPZrNTUVMIPAMBwWAEKMf6GGcIPAMCICEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCECAgTgcjqCeDwDNBQEIMAir1aq0tDTZ7Xafzrfb7UpLS5PVag1uYQDQCAhAgAE4HA7ZbDZJksViqTUE2e12WSwWSZLNZmMlCEDIIQABBmAymZSVleX5eU0hqHL4kaSsrCyZTKag1wgADYkABBiE2WyuNQR5Cz9ms7nBagSAhkIAAgykphBE+AFgJC0buwAADcsdatxhx2KxaN68eSouLvacQ/gBEOr8CkC///3vNWvWLPXs2TNY9QRMSUmJlixZopycHB05ckStWrXSLbfcoscee0zXX3+9X3M99dRT+uCDDy47/uCDD2rWrFn1LRloMNVDEOEHgNH4FYC2b9+uUaNG6d/+7d/05JNPKiYmJlh11UtpaakeffRRbdmyRddcc41uv/12HT9+XGvXrlVubq4WL16s1NRUn+fbvXu3JOnuu+9WixaXfmrYp0+fgNUONBSz2XzJyk9sbCzhB4Ah+BWAHnjgAb399tt6++23tWbNGj355JMaPXq0wsLCglVfnSxatEhbtmyRyWTSggULFBUVJUlavXq1zGaz/vznP+vjjz9W69ata53r3Llz+vbbb3XNNdcoOzs72KUDDcZut1cJP1LFSpDdbicEAQh5fm2CnjVrllauXKnk5GSdPXtWmZmZSk9P19atW4NVn9+cTqeWLFmiFi1aKDMz0xN+JOnee+/V8OHDdfr0aa1atcqn+fbs2aOLFy+qd+/ewSoZaHDVNzzHxsZ6fuxLnyAAaO78fgrs+uuv17Jly2S329W+fXvt2bNHY8aM0Z///GedPHkyGDX65YsvvtBPP/2kXr16KT4+/pLxO++8U5KUm5vr03y7du2SJAIQQoa3p72Kiop87hMEAKGgzo/B33vvvfroo480fvx4hYeHKycnR3fddZdeffVVlZeXB7JGv+Tn50uSEhMTvY53795dkrR3716f5vvmm28kSeHh4Zo+fboGDRqkPn366O6779aiRYtUWloagKqBhlHTo+6+9AkCgFBRrz5ArVu3ltls1urVq/Xb3/5W586d0wsvvKB77rmn0Vrnu1ehOnbs6HXcffz06dO6ePFirfO5N0BnZ2dr+/bt6tWrl2644QYdPnxYL774osaMGaOffvopQNUDweNLnx9CEACjCEgfoG7duum//uu/tHbtWtntdh06dEiPPvqoBg8eLIvFoi5dutR57smTJysvL8+nc9etWyen0ylJatWqlddzIiMjPT92Op1q06bNZec7f/68Dh06JKniUfiJEyd6ngI7ePCgpk6dqp07d2rOnDmaM2eOTzUCjcHhcPjc5NBbn6DU1FRehwEgpAS0E/TgwYM1Z84cxcfHy+VyKTc3VyNGjNBLL71U54+K2rVrp/j4eJ/+a9mypcLDw2ucr/ITay6Xq8ZzW7VqpU2bNunDDz/UpEmTqjwCf91113n+Zbxq1SqdPXu2TtcHNASTyaSMjAxJvvX5qbwSlJGRQfgBEHLqtQJ05MgR7dixQ1999ZV27typvXv3qqyszDPucrlUWlqqhQsX6v3331dmZqb69+/v1/fwd2XF/Wh7SUmJ1/HKxys/IXY5MTExl+13dOONNyouLk6FhYX65ptv/L42oCFZrVYNHTrU5zBjNptZ+QEQsvwKQBs3btSOHTu0c+dO7dixQ99//71nzL2aEh4ersTERCUnJ+umm25SVFSU5s+fr3379umRRx7RY489pilTpgT2Kipx7/E5deqU1/ETJ05IqnjsNyIiot7fr1OnTiosLNT58+frPRcQbP6GGcIPgFDlVwB65JFHFBYWVuWjoyuvvFJ9+vRRcnKykpOT1bdvX0VHR1f5usGDB2vJkiV64YUXtGDBAnXu3Fnp6emBuYJqkpKSJEn79+/3On7gwIEq59Xks88+04oVKxQfH69p06Z5Pef48eOSKoIQAABoHvz+CCwhIcGzupOcnKwePXrU2gm6RYsWGjdunNq3b6+nn35ay5YtC1oA6tevn9q0aaOvv/5ahYWFiouLqzL+0UcfSZIGDhxY61wul0s5OTmKjo7Wo48+esmG6c2bN3u+hy+BCgAANA1+bYLeuHGjPvnkE9ntdo0ePVqJiYl+vQZjxIgRatOmjQ4ePOh3ob6KjIzU/fffr/LyclksliqPqL///vv66KOP1LZtW91///1Vvu7YsWMqKCio8mqAlJQUde/eXU6nUxaLxfOEmVSxwjRjxgxJ0tSpU72+IwwAADRNfq0AtWvXrt7f8KqrrvJ8bBQsU6dO1ZYtW7R582YNGzZMt9xyiwoLC7Vjxw5dccUVevHFFy/5mM5sNmvLli2aMmWKpk6dKqli5So7O1vjxo3TJ598oqFDh6pv375yOp368ssvVV5errFjx2rUqFFBvR4AABBYAekD5I+MjAxt27YtqN8jOjpaS5cu1SuvvKL/+Z//0fr169W2bVvdcccdevzxx3X99df7PFdSUpJWr16txYsXKy8vTxs2bFB0dLRSUlL04IMPasiQIUG8EgAAEAxhrtqa4aBBpaena/fu3erVq5fefffdxi4HAIBmw5+/Q9m4AgAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADMcwAWjChAm66aab6vS15eXlevvtt5Wenq7k5GTdeuuteuSRR/T5558HuEoAANAQDBGA7Ha7Nm7cWKevdblcMpvNmjVrlo4eParbbrtNiYmJ2rRpkx5++GGtXLkywNUCAIBga9nYBQST0+mUzWbTqlWr6jzHypUr9cEHH6hnz556/fXXFRMTI0navHmzJk+eLJvNpttuu02dOnUKVNkAACDIQnIFyOVyac2aNbr33nu1atUqdenSpc5zLV68WJL0zDPPeMKPJPXv318PP/ywSktLtXTp0nrXDAAAGk5IBqDvvvtOTz75pI4dO6YJEyZ4Qoy/Dhw4oMOHD6tdu3bq16/fJeN33nmnJGndunX1qhcAADSskPwILCIiQunp6Zo0aZK6du2qo0eP1mmeffv2SZJ69OihsLCwS8bdxw8fPqzz58+rVatW9aobAAA0jJBcAerYsaPmzp2rrl271muekydPeubzJjIyUldddZUuXryo06dP1+t7AQCAhtPkV4AmT56svLw8n85dt26dEhISAva9z507J0mKioq67DmRkZFVzgUAAE1fkw9A7dq1U3x8vE/ntmwZ2MsJDw+XJK8ffwEAgOaryQegOXPmNNr3bt26tSSppKTksueUlpZKEvt/AABoRkJyD1CguPf+nDp1yut4aWmpfvjhB4WFhemaa65pyNIAAEA9EIBqkJSUJEnav3+/1/H9+/fL5XKpS5cuio6ObsjSQpLD4Qjq+QAAuBGAavDrX/9a1157rU6ePKmvvvrqkvGPPvpIkjRw4MAGriz0WK1WpaWlyW63+3S+3W5XWlqarFZrcAsDAIQkAtAvjh07poKCAhUXF1c5PnbsWEnSs88+W+VR982bN2vJkiWKiIjQhAkTGrTWUONwOGSz2SRJFoul1hBkt9tlsVgkSTabjZUgAIDfCEC/MJvNGj58uJYtW1bl+O9//3sNHDhQ+/bt05133qnHHntMDz30kCZMmKCff/5Zzz33HO8BqyeTyaSsrCzPz2sKQZXDjyRlZWXJZDIFvUYAQGhp8k+BNbYWLVro5Zdf1htvvKF3331XDodDbdq00W233abJkyfr1ltvbewSQ4LZbJYkT7hx/6/7uOQ9/FQeBwDAV4YIQAkJCcrPz6/xnJpeaBoREaHx48dr/PjxgS4NldQUggg/AIBAMkQAQvPhLQTNmzevyt4swg8AoL7YA4Qmx2w2V9kTRPgBAAQaAQhNktlsVmxsbJVjsbGxhB8AQEAQgNAk2e32S1oSFBcX+9wnCACAmhCA0ORU3/BceSXIlz5BAADUhgCEJsXb015FRUU+9wkCAMAXBCA0GTU96l59YzQhCABQHwQgNAm+9PkhBAEAAoUAhEbncDh8bnLoLQTxLjAAgL8IQGh0JpNJGRkZknzr81M5BGVkZPAuMACA3+gEjSbBarVq6NChPocZs9ms1NRUwg8AoE5YAUKT4W+YIfwAAOqKAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAyHAAQAAAynZWMX0FAmTJig7du3a/v27X5/7VNPPaUPPvjgsuMPPvigZs2aVZ/yAABAAzJEALLb7dq4caOio6Pr9PW7d++WJN19991q0eLSRbM+ffrUqz4AANCwQjoAOZ1O2Ww2rVq1qs5znDt3Tt9++62uueYaZWdnB7A6AADQWEJyD5DL5dKaNWt07733atWqVerSpUud59qzZ48uXryo3r17B7BCAADQmEIyAH333Xd68skndezYMU2YMEGLFy+u81y7du2SJAIQAAAhJCQ/AouIiFB6eromTZqkrl276ujRo3We65tvvpEkhYeHa/r06dq+fbuKiorUpUsX3XPPPRo/frwiIyMDVToAAGgAIbkC1LFjR82dO1ddu3at91zuDdDZ2dnavn27evXqpRtuuEGHDx/Wiy++qDFjxuinn36q9/cBAAANp8mvAE2ePFl5eXk+nbtu3TolJCQE7HufP39ehw4dklTxKPzEiRM9T4EdPHhQU6dO1c6dOzVnzhzNmTMnYN8XAAAEV5MPQO3atVN8fLxP57ZsGdjLadWqlTZt2qTTp0+re/fuVcauu+462e123XfffVq1apXMZrOuvvrqgH5/AAAQHE0+ADX2ykpMTIxiYmK8jt14442Ki4tTYWGhvvnmG/Xv37+BqwMAAHURknuAGlKnTp0kVXxcBgAAmocmvwLUmD777DOtWLFC8fHxmm0jcqUAABAVSURBVDZtmtdzjh8/LumfQQgAADR9rADVwOVyKScnR0uWLPH6pNfmzZtVWFiouLg4JSUlNUKFAACgLghAvzh27JgKCgpUXFzsOZaSkqLu3bvL6XTKYrHI6XR6xvbv368ZM2ZIkqZOner1HWEAAKBp4iOwX5jNZm3ZskVTpkzR1KlTJUktWrRQdna2xo0bp08++URDhw5V37595XQ69eWXX6q8vFxjx47VqFGjGrl6AADgDwJQLZKSkrR69WotXrxYeXl52rBhg6Kjo5WSkqIHH3xQQ4YMaewSAQCAnwwRgBISEpSfn1/jOUuXLr3sWIcOHfTss8/q2WefDXRpAACgEbBxBQAAGA4BCAAAGA4BCAAAGA4BCAAAGA4BCAAAGA4BCAAAGA4BCAAAGA4BCAAAGA4BCI3O4XAE9XwAAKojAKFRWa1WpaWlyW63+3S+3W5XWlqarFZrcAsDAIQ0AhAajcPhkM1mkyRZLJZaQ5DdbpfFYpEk2Ww2VoIAAHVGAEKjMZlMysrK8vy8phBUOfxIUlZWlkwmU9BrBACEJgIQGpXZbK41BHkLP2azucFqBACEHgIQGl1NIYjwAwAIhpaNXQAgyRNq3GHHYrFo3rx5Ki4u9pxD+AEABAorQGgyqq8EEX4AAMFCAEKTYjabFRsbW+VYbGws4QcAEFAEIDQpdru9ysqPVLES5GufIAAAfEEAQpNRfcNz5ZUgX/oEAQDgKwIQmgRvT3sVFRX53CcIAAB/EIDQ6Gp61N2XPkEAAPiLAIRG5UufH0IQACDQCEBoNA6Hw+cmh95CEO8CAwDUFQEIjcZkMikjI0OSb31+KoegjIwM3gUGAKgzOkGjUVmtVg0dOtTnMGM2m5Wamkr4AQDUCytAaHT+hhnCDwCgvghAAADAcAhAAADAcAhAAADAcNgE3cQcPXpUklRQUKD09PRGrgYAgOajoKBA0j//Lq0JAaiJKS0tlSSVlJRo9+7djVwNAADNj/vv0poQgJqY2NhYFRcXKzIyUgkJCY1dDgAAzcbRo0dVWlpa5WXalxPmcrlcDVATAABAk8EmaAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgEIAAAYDgtG7sABMahQ4e0YMECbd26VUVFRYqLi9Ndd92lyZMnKzo62q+58vLy9MYbb2jXrl368ccfFRMTo+TkZE2cOFF9+/YN0hUYUyDvW3V2u12vvfaapkyZoqlTpwaoYrgF8t45nU699tprWrt2rQ4fPqwWLVqoZ8+eGjt2rP7lX/4lSFdgTIG8b1999ZUWL16sbdu26dy5c2rXrp1uu+02/eEPf9CvfvWrIF0BAiXM5XK5GrsI1M/OnTv18MMPy+l0qk+fPurUqZO2bdumU6dOKSkpSX//+9/Vpk0bn+bKzs7W4sWLFRYWpl69eikuLk4HDx7UwYMHFR4ertmzZ2vkyJFBviJjCOR9q27jxo165JFH5HK5CEBBEMh7d/r0aT388MM6cOCA2rdvr9/85jcqKirSV199JZfLpRkzZmjcuHHBvSCDCOR9W7NmjZ566ilduHBBvXr1UufOnZWfn6/Dhw+rdevWev3119WnT58gXxHqxYVmrayszDVkyBBXYmKia/ny5Z7j58+fd/3Hf/yHKzEx0WWz2Xya64svvnAlJia6+vbt6/rss8+qjL355puuxMRE14033uj67rvvAnoNRhTI+1ZdUVGRKzU11ZWYmOhKTEx0zZ8/P1BlwxX4ezdp0iRXYmKia+rUqa6SkhLP8Y0bN7p69erl6tmzJ7/nAiCQ983pdLpuvvlmV1JSkisnJ8dzvLy83DVnzhxXYmKia8SIEQG/BgQWe4CauQ8//FBHjhxR//79NWrUKM/xqKgozZkzR9HR0XrnnXd09uzZWudasWKFJGnixIlKSUmpMjZ69GgNGDBAP//8s9auXRvYizCgQN636v7f//t/OnPmjJKTkwNZMn4RyHu3c+dO5eXl6Ve/+pWef/55RUZGesZuu+02paenKy4uTrt27QrKtRhJIO/bV199pR9++EE9evTQiBEjPMfDw8M1bdo0hYeHa9++fSouLg7KtSAwCEDNXG5uriRp2LBhl4y1bdtWKSkpKisr04YNG2qdKyoqSomJifrtb3/rdfy6666TJJ04caIeFUMK7H2rbNmyZVq/fr0ef/xx3XjjjQGpFVUF8t6tWbNGkvTQQw9VCT9umZmZys3N1R133FHPqhHI+xYeHi5JKi4u1s8//1xl7MyZM7pw4YIiIiLq/BE2GgYBqJnbt2+fJCkpKcnrePfu3SVJe/furXUuq9WqnJwc3XzzzV7Hd+zYIUmKi4urS6moJJD3zW3//v2y2+1KTk7W5MmT618kvArkvXOv7PzmN7+R0+nUe++9p8zMTGVkZGjFihUqKSkJUNUI5H3r3bu3YmNjdfr0aT311FM6ePCgSkpKtGPHDj3++OOSpHHjxumKK64IUPUIBp4Ca+ZOnjwpSerYsaPX8Q4dOlQ5r65yc3O1bds2RUREeP0XFPwT6PtWWlqq6dOnKyIiQs8//7znX6gIvEDeu3/84x+SKlYNRowYoe+++84z9tZbb+lvf/ubFi1apB49etSzagTyvrVq1Uovv/yypk2bpo8//lgff/yxZywqKkqZmZn693//9wBUjWBiBaiZczqdkip+03njPu4+ry7y8/M1Y8YMSRX7g+Lj4+s8FyoE+r7NmzdP+/bt07PPPquEhITAFAmvAnnvfvrpJ0nS008/rSuvvFJvvPGGtm7dqtWrVystLU1Hjx7Vo48+6jkPdRfo33Ndu3bVv/7rvyo8PFy9evXSkCFD1KVLF5WUlOj111/X119/HZjCETSsADVz4eHhunjxosLCwmo8z1XHbgc7d+7UpEmT9P3332vQoEF64okn6jQPqgrkfXP3bRo+fLh+97vfBapEXEYg711paakk6YorrtCSJUt09dVXS5Kuv/56LVq0SCNHjtS+ffv01ltvaeLEifUv3sACed+OHz+uMWPG6MyZM3r11VfVv39/z9f+93//t+bOnavx48crJydHnTp1Ckj9CDxWgJq51q1bS5LOnz/vddy9h6BVq1Z+z/3RRx9p7NixOnPmjIYOHar58+erRQv+LxMIgbpvp0+f1owZM9SpUyfZbLbAFgmvAvl7zr3q8Lvf/c4Tftxatmyp0aNHS5I2b95c53pRIZD37cUXX9TRo0f1xBNPeMKPJIWFhWncuHG655579OOPP+r111+vf+EIGlaAmrkOHTro+++/16lTp9SlS5dLxt2fZ7s/3/bVggUL9NJLL8nlcumBBx7QM888w76SAArUfVu4cKGKi4vVs2dPZWZmVhnbvXu3JOnjjz/Wt99+q27duukPf/hDgK7AuAL5e659+/Y6d+7cZT+2dB8/c+ZMPSqGFNj7tmnTJklSWlqa1/GBAwcqJyeH9gVNHP+cb+bcTzQcOHDA67j7+OWefKju4sWLslgsntWemTNnKiMjg/ATYIG6b+79Cnv27FFOTk6V/w4ePCip4umXnJwczx/aqJ9A/p5zn3O51hKnTp2SJMXGxvpdJ6oK5H1z9wpq2dL7GoL7z8vy8nK/60TDIQA1cwMGDJAkr80Jz5w5o88//1wRERFKTU31ab5nnnlG7733nqKjo/W3v/1NY8eODWi9qBCo+5aVlaX8/Hyv/7nv3ZQpU5Sfn6+lS5cG/kIMKJC/5wYOHCipoh9QWVnZJeP/93//J0m69dZb61ExpMDet27dukn6Z2+h6hwOhySpZ8+edS0XDYAA1MwNGzZMnTt3lsPh0LJlyzzHS0pKNHPmTDmdTo0aNUrt27f3jJWVlamgoEAFBQVV/tBdtWqVVq5cqZYtW2rhwoWePzAQeIG8b2hYgbx3w4cPV0JCgv7xj38oMzOzytjy5cu1du1aXX311brvvvsa5uJCWCDv24MPPihJevnll/XFF19U+T4rVqzQypUrFRERoTFjxgT5qlAfvAw1BHz++eeaNGmSSkpK1KtXLyUkJGj79u06efKkbrjhBi1durRKR9KjR49qyJAhkqR169YpISFBFy5c0JAhQ3T8+HF17Nixxn9xmkwmnjYKgEDct5rMnj1bS5Ys4WWoQRDIe7dr1y5NnDhRZ86cUYcOHdS3b199++232rdvnyIjI/XXv/5VgwcPbvBrDEWBvG+zZs3S22+/LamiMWJcXJwOHDigQ4cOKSIiQrNnz9a9997bsBcIv7AJOgSkpKRo+fLlevnll7VlyxYdOHBACQkJGjVqlB555BGf2rHn5+fr+PHjkir2I+Tk5Fz23KuuuooAFACBuG9oHIG8dzfeeKNycnK0ePFirV+/Xnl5eYqJidHdd9+tSZMm6frrrw/ilRhLIO9bZmambr/9dr355pvatWuX9uzZo7Zt22rEiBGaOHEiH381A6wAAQAAw2EPEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEAAAMBwCEABcxtatW5WUlKSkpCStWbPG6zk7duzQTTfdpKSkJM2bN6+BKwRQVwQgALiMfv36afDgwZKk+fPn68KFC1XGDx48qMmTJ8vpdGrkyJH605/+1BhlAqgDAhAA1ODpp59WeHi4Dh48qPfff99z/MSJE5o4caLOnDmjQYMG6bnnnlNYWFgjVgrAHwQgAKhBt27dNHLkSEnSyy+/rLKyMv3www+aOHGivvvuO/Xr109//etf1bJly0auFIA/wlwul6uxiwCApuzEiRO64447VFJSohkzZujTTz/VF198ocTERC1btkxXXXVVY5cIwE8EIADwwQsvvKBXXnnF8/P4+Hi9+eab6tixYyNWBaCuCEAA4IOTJ09qwIABunjxomJiYvT222/r2muvbeyyANQRe4AAoBbl5eWaNWuWLl68KEk6f/68oqKiGrkqAPVBAAKAGrhcLj3zzDNav369YmNjlZCQoNLSUs2fP7+xSwNQDwQgAKjBvHnz9N577yk6OlqLFy/WtGnTJEmrVq3SgQMHGrk6AHVFAAKAy3j11Vf12muvKSIiQi+99JL69Omju+++W0lJSbpw4YL+8pe/NHaJAOqIAAQAXqxatUrPP/+8wsLCNHfuXJlMJklSWFiY/vjHP0qScnNztXXr1sYsE0AdEYAAoJr//d//1cyZM+VyuWSxWHTPPfdUGR8yZIj69u0rqeLxeADNDwEIACrZvn27/vjHP6q8vFyPPvqoxo0b5/U8916gbdu26dNPP23ACgEEAn2AAACA4bACBAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADIcABAAADOf/A6up2XWuqMFJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fixing the seed so that we all see the same data\n",
    "np.random.seed(1234)\n",
    "n = 10\n",
    "# The inputs are in [0, 1]\n",
    "X = np.random.rand(n, 1) # Needs to be an n x 1 vector\n",
    "# The outputs are given from a function plus some noise\n",
    "# The standard deviation of the noise is:\n",
    "sigma = 0.4\n",
    "# The true function that we will try to identify\n",
    "f_true = lambda x: -np.cos(np.pi * x) + np.sin(4. * np.pi * x)\n",
    "# Some data to train on\n",
    "Y = f_true(X) + sigma * np.random.randn(X.shape[0], 1)\n",
    "# Let's visualize the data\n",
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  \u001b[1mrbf.       \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mvariance   \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mlengthscale\u001b[0;0m  |    1.0  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "# Now, we will get started with the regression\n",
    "# First, import GPy\n",
    "import GPy\n",
    "# Second, pick a kernel. Let's pick a squared exponential (RBF = Radial Basis Function)\n",
    "k = GPy.kern.RBF(1) # The parameter here is the dimension of the input (here 1)\n",
    "# Let's print the kernel object to see what it includes:\n",
    "print(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ``variance`` of the kernel is one. This seems reasonable.\n",
    "Let's leave it like that.\n",
    "The ``lengthscale`` seems to big.\n",
    "Let's change it to something reasonable (based on our expectations):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  \u001b[1mrbf.       \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mvariance   \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mlengthscale\u001b[0;0m  |    0.1  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "k.lengthscale = 0.1\n",
    "print(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a possibility to choose a mean function, but for simplicity we are going to pick a zero mean function:\n",
    "$$\n",
    "m(x) = 0.\n",
    "$$\n",
    "Now we put together the GP regression model as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "gpm = GPy.models.GPRegression(X, Y, k) # It is input, output, kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model is automatically assuming that the likelihood is Gaussian (you can modify it if you wish).\n",
    "Where do can you find the $\\sigma^2$ parameter specifying the likelihood noise? Here it is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 13.029643687983668\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |    1.0  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "print(gpm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will talk about the meaning of all that later. For now, let's just fix the noise variance to something reasonable (actually the correct value):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 13.142900653688129\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |                  1.0  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |                  1.0  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.16000000000000003  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "gpm.likelihood.variance = sigma ** 2\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's it. We have now specified the model completely.\n",
    "The posterior GP is completely defined.\n",
    "Where is the posterior mean $m_n(x)$ and variance $\\sigma_n^2(x)$? You can get them like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HN9XKFTh6LQ9fnc5AzNU83L/a19veEvNGeGPOcE842XSvCs1dRS8D0LVr1wDULeZUJyAgADExMUhKSmoxAFVVVSElJQU9e/bEqVOnsGfPHiQnJ0OhUGDQoEF47rnnEBIS0uGfgYioo2hSpFSTYqfU/RXcrcS35zKx+0wGbt6uUGkTGgkwtZ8LFozyRoi/o0HN9qijlwEoLy8PQN2hl+o4Ozur3NecpKQkVFdXo7i4GG+88QaGDBmCkSNHIjk5GSdPnsTJkyfxyiuvYPny5R33AYiIOlhzIYjhR7cpFApcyLiNnadu4NdLOaiqVa3S7GZrjnkjvPFksBdcDGBtj6b0MgCVl9cVbDI3V/9/dP31+vuac+XKFQB1oWnLli0qj8F++OEHvPnmm9i4cSOGDh2K4ODg9g6diKjTqAtBGzZsQFFRkfIehh/dUV5Vgx/js7Hz9A0k3rqj0iYQAON6O2HhKB9MDHSCsZClLe6nlwFIKBRCLpe3ePq3JiWQ5s6di3HjxkEoFDaaUXrsscdw+fJl7Ny5Ezt27GAAIqJu7/4QxPCje9IKyrDz1A18dz4TpbIalTY7SxPMfcALC0b6wNuh+9ft0Sa9DEBWVlYoLi5GRUWF2naZTAYAsLCwaLEvIyOjZo8lmDx5Mnbu3Kms9ktE1N2JxeJGMz/29vYMP91YrVyB2Kt5+PLUDRy7lt+ofah3Tzw9ygczgtxgbiLUwgh1j14GIGdnZxQXFyM/Px9eXl6N2uvX/tSvBWoPV1dXAGgybBERdTcSiUQl/AB1M0ESiYQhqJspKa/Gt+cyseN0OjKLVH/PmBkbYfYQdywa7av2WApqnl4GoMDAQFy7dg3JyckYNmxYo/bk5GTlfS3ZsmULkpKSMG/ePOW5Tw3l5OQAuBeEiIi6s/sXPNvb2yvDkCZ1gqhrJOXcwZcn0/FDfBZk1aqLmr3sLfD0KB88MdwLdlamWhqh7tPLVVHjx48HABw6dKhR2+3bt3HmzBmYmJhotH09LS0Nhw4dwg8//KC2vf76hAkT2j5gIqIuoG63V2FhIaKiopTXwsLCIJFItDE8g1crV+DQ5RzM234aD75/HF/HZaqEn7G9HfHp4gcQ++pELB/nz/DTTno5AzR16lS4u7tDKpVi165dWLBgAYC6tT9vvvkmysvLMW/ePDg6OipfU11djYyMDACAt7c3TExMAADz58/HgQMHsH//fohEIjzyyCPK1+zYsQM//fQTevbsiUWLFnXhJyQiap3mtrprUieIOk9JeTX2nMvAlydvIKtY9TGXtZkx5gz3xNOjfeDvpNn5laQZvQxA5ubmiIqKwvLly7Fu3Trs3bsXnp6eiI+PR15eHvr3749XX31V5TW5ubmYMWMGAODIkSPw9PQEAAwdOhQvv/wy3nvvPbz22mv49NNP4ePjg+vXryM1NRWWlpbYvHkzHBwcuvxzEhFpQpM6PwxBXS85rxSfn0jHvgtZqKiuVWnr5WiFxWN8ETrMAzbmJloaoX7TywAEACNHjsR3332HTZs2IS4uDsnJyfD09MScOXOwdOlSjU+CB4Dly5cjKCgIn3/+ORISEpCSkgInJyfMnTsXzz//PDw8PDrxkxARtZ1UKtW4yKG6EBQSEsLjMDqQXK7Asev5+OxEutrdXOP7OGFJiC/G9XYy+ErNnU1vAxAA9OnTBx988IFG93p6euLq1atNto8ePVrtImgiou5MJBIhPDxc49PgG4ag8PBwhp8OUl5Vg30XsvD5iTSk5JeptFmaCvHEcE8sGuPLx1xdSK8DEFF3V15ejmnTpsHS0hK//fYbhMK21++oqKjA5MmTYWNjg59//lm5jo0oIiKiVae6i8Vizvx0kFslFfjy5A18HZeBkopqlTYvewssHu2LucFe6MHHXF2OAYhIiz7++GPk5+dDIpG0K/wAdYU9n3vuOUgkEnzzzTd4+umnO2iUpA9aG2YYftonIbMYn0rT8OulW6iRq546MNLPHs+K/DClnwuEfMylNQxARFpSUFCAzz//HD4+Ppg1a1aH9Dlv3jxs374dmzdvRmhoKKysrDqkXyJqWa1cgcNXcvGpNBVn02+rtJkIBXhksAeWhLBoYXfBAESkJd9++y0qKioQGhra7tmfehYWFpg5cya++uorHDhwAE899VSH9EtETSurrMF35zLx2Yl0ZBSpHrJtb2WKhSO9sXC0D5xteBJ7d8IARKQFcrkc33//PQQCQYfN/tSbPXs2vvrqK+zZs4cBiKgT5ZTI8OWpdOw6fQN37juUNMDZGs+J/PDoUA+ezdVN6WUlaKKWTJ8+HYGBgYiPj0dSUhJeeeUVhISEYMiQIXjiiSdw8uRJ5b3p6el46623MGHCBAwZMgShoaGIiYlp1/ufP38eWVlZ6Nu3b5NlFL744gsEBgZi4sSJqKqqatR+4cIFDBo0CP3798cff/yhvD5o0CA4OTnhypUrSElJadc4iaixK9l38PKePyGSROOj2BSV8DO2tyO+WBKMwy+Nw1MjvBl+ujEGIDI4FRUVyMjIgEAgwKVLlzBnzhycPn0aLi4uEAgEuHjxIlasWIHr16/j0KFDeOyxx/D777/D3t4exsbGuHz5MlauXInLly+3eQxnzpwBUBdWmjJ//nx4eHggOzsb3333nUpbSkoKXnjhBVRWViI8PBxTpkxRaa/vt/59iKh9FAoFjl7Lx9OfnsGMD45jX3yWcnGziVCAOcM9cfAfY7Fz6UhMCHSGQMDFzd0dAxAZnKSkJMjlcggEArz//vv4z3/+A6lUin379uHw4cPw9PREVVUV1q9fj7CwMLz44os4ceIE9u3bh9jYWAQFBUEulzcKJa1x/vx5AEBQUFCT95iammLNmjUAgK1bt6KyshIAkJeXh2XLlqG4uBhr1qzBk08+2ei19QGo/n2IqG2qauT4/vxNPPT/jmPxZ3E4fr1A2WZrYYJVE/1xQjwJ7z4xGH1de2hxpNRaXANkAH65eAsbD19FWWVtyzd3M1ZmQrwyLRAzgtw6rM/ExEQAdetw/vOf/yiPQAEAR0dHPPLII9iyZQtOnjwJsViMZ555RtlubW2NuXPn4tKlS7h582abx5CVlQUAcHJyava+2bNn49NPP8X169fx9ddfY86cOVi+fDmysrLw1FNPYfXq1Wpf5+zsrPI+RNQ6d2TV2H0mA5+fSEPunUqVNh8HSywV+WHOcE9YmvLXqK7i/3MGYPuxlEaVR3XJtmOpHRqAkpKSAABjx45VCT/1TE3rTlju06cPlixZ0qi9fseWmZlZm8dQVFQEALC1bX47rJGREV566SWsXLkS27dvR0xMDBITEzF16lSEh4c3+br6fuvfh4g0c6ukAp9J0/B1XCbuVqoubB7m3RPLx/XC1P6urN+jBxiADMCK8f5473fdnQFaMa5Xh/ZZPwP08MMPq21PS0sDADz44INqn+Onp6cDALy9vds8BplMBkCzEDV58mQMHToU8fHxKCwsRHBwMN577z0YGTX9BNvcvG67bUVFRZP3ENE9STl3sP1YKvb/ma1SuFAgAKb2c8GK8b0w3MdeiyOkjsYAZABmBLl16AyKLpPL5bh+/TqAugNz1bly5Uqz7fUBqn///m0eR8+ePZGfn4+SkpIW762pqYGlpaXyzxERES0Gp/p+7ezs2jxGIn2nUChwJq0I246mIOaq6sGkpsZGmDPcE8+J/NCL53PpJQYgMihpaWmoqKiAnZ0d3Nwah8LKykqkpqZCIBCgb9++avtoKgDNnDkTQ4YMwejRo/HZZ58hOTkZnp6eWLt2LUaNGqVyr6OjI/Lz81FcXNzseBUKBd58802cOHECxsbGqKmpwY4dO7Bu3bpmX3f7dl0VWgcHh2bvIzJEtXIFfr+cg63HUpGQqfodtLUwwaLRPlg02hdONm1/zE3dHwMQGZSWZm+uXr2K2tpa+Pr6wtq68d/68vLyUFBQAAsLC/j6+iqvV1ZWIi0tDTKZDDk5OXj++edhYmKC//73v3jttddw/PhxlX769++PxMREJCcnNzved999Fz/++CN8fX3x9ttvY9GiRdi7dy+WLFkCPz+/Jl9X3++AAQOa7Z/IkMiqa7HvQhY+Pp6KtALVdZEePS2wbKwf5gZ7cWGzgeA2eDIo9QGoX79+atvra/s01V7/+sDAQJXjK+qDU9++ffHpp59i2rRpmDhxIhYvXoy8vDzcvXtXpZ8RI0YAABISEpoc6xdffIFPPvkETk5O+OSTT/DAAw/g4YcfRk1NDd5///1mP2d9v8HBwc3eR2QI7siq8VFsCsZuiME/f7ikEn76ufXA/3tqCI6+NgHPhPgpw49UKm3Ve7T2ftI+BiAyKPU7wJqaGWlphqipAFV//cUXX1S5fvv2bVhYWDQ6lHTMmDEQCoVISEhAdXV1o/f55ZdfEBUVBSsrK2zfvh1eXl4AgDVr1sDY2BiHDh3CX3/9pXaMpaWluHbtGiwtLfHAAw+ovYfIEOTdkSHqtySEvBMNycEk5Jfe284+xt8BO54dgV//T4TZQzxgLLz36zAiIgJjx46FRCLR6H0kEgnGjh2LiIiIjv4I1IkYgMig1AegpmZ46hdANxWAmmpPTEyEq6sr+vTp0+j+Pn36NNpN5uzsjAkTJuDOnTs4evSoSlt9/SFjY2Ns2rRJ5b28vLwQGhoKhUKB9957T+0YDx48iOrqasycOZOnwZNBSi8owxv7LkEkicHWoyko/Xs7u0AAzAhyxf7VIdi9bBTG9XFq9N2USqWIjIwEAISFhbUYgiQSCcLCwgAAkZGRnAnSIQxAZDAKCgpQUFAAKysrlfU79WpqanDt2jUAbZsBUjerlJiY2GRf9QeV7t+/X3ntypUrWL16NWpqarB+/XqMGTOm0etWrlwJU1NTnDx5EqdOnWrUXt+fugrRRPrsr6wSrNp9AZPei8XXcRmoqpUDAEyFRpg3wgtHXh6PLQuGY5Bnzyb7EIlEiIqKUv65uRDUMPwAQFRUFEQiUQd9GupsXOlFBsPR0RFXr15tst3Y2BgXL15sto/Dhw83uiaXy3Ht2jUsXbpU5frdu3eRmZnZ5OO2cePGYfDgwThy5AgyMzPh5eWF/v3748KFC82Owc3NDZcuXVLbdvnyZcTFxWHChAnNHrNBpC/qt7J/FJuCo9dUt7JbmxljwShvLA3xg3MPc437FIvFAKAMN/X/rL8OqA8/Ddup+2MAImqntLQ0lJeXY+DAgSrXExMToVAomq0XJBaLMX/+fGzZsgXvvPNOu8fy4YcfQigU4vXXX293X0TdmUKhwJHEPGyJTcaFDNWt7I7WplgS4oeFo3xga2HSpv6bC0EMP/qBAYionerXFd0fdK5cuQITExP07t27ydcOHz4cERERKC4uRm1trcrOstaqqKjAwIED8eCDD8Lf37/N/RB1ZzW1cvxy6Ra2xKTgam6pSpunnQVWjOuFJx7wgrlJ279L9dSFoA0bNqgcMcPwo7sYgIjaaebMmZg5c2aj64sXL8bixYtbfP28efM6ZBwWFhZNHo5KpOtk1bXYe+Emth1NRUZRuUpbHxdrvDDBHw8PcoeJsGOXtt4fghh+9AcDEBERdVtllTXYfSYDHx9PRV6p6qnsQ717YuWEAEzu6wyjTjycVCwWN5r5sbe3Z/jRcQxARETU7RSXV+HLkzfw+ck0FJer1soa29sRKycEYFQve7UHFnc0iUSiEn6AupkgiUTCEKTDGICIiKjbyC+txCfSVHx16gbKqmpV2h4c4IqVE/2b3cbe0e5f8Gxvb68MQ+p2h5HuYB0gIiLSuqziCoT/9BdEkmhsO5qqDD9CIwFCh3rg8EvjsPXp5mv4dDR1u70KCws1rhNE3RtngIiISGtS8+/io9gU/BCfhRq5Qnnd1NgIcx/wxIpx/vCyt+zycTW31V2TOkHU/TEAERFRl0vKuYPNMSn45WI2GuQeWJoKsWCkN5aN7dWq4oUdSZM6PwxBuo8BSIc1XPwnl8thZMQnmtQ2tbX31lp0xaJSMlwJmcXYFJOMw1dyVa7bmBtjyRhfLAnxg52VqZZGV3cWmKZFDtWFoJCQEB6HoSMYgHSYQCCAqakpqqqqUFZWBltbW20PiXTUnTt3AABmZmYMQNQpzqYX4cPoZEQAeDsAACAASURBVBy777gKeytTLBX54enRPuhh3raqzR1JJBIhPDwckZGRGtX5aRiCwsPDGX50CAOQjrOxsUFhYSFyc+v+NmVlZcWZINKIQqFAZWUlSktLlbta7OzstDwq0icKhQKnUgrxQfR1nE5V3Ubu0sMMK8b5Y94Ib1iYtr9qc0eKiIjAlClTNA4zYrGYMz86iAFIxzk4OKCsrAwymQzZ2dnaHg7psJ49e3IWkTqEQqFA7LV8fHjkeqNzujztLPDCBH/MGe4JM+PuFXwaam2YYfjRPQxAOk4oFMLb2xuFhYUoLS1FVVWVtodEOkQoFMLKygo2NjawsbHh4y9qF7lcgcOJudgUnYxLWSUqbb0crbByYgBmD+n44yr0kVQqbVWoau39xACkF4RCIZydneHs7AyFQgGFQtHyi8jgCQQCBh7qELVyBX776xY2RScjKUf1gNI+LtZYPak3Zga5QdiJx1Xok4iICI3XIAH3dq2Fh4cjIiKi8weoJxiA9Ax/qRFRV6mplePAxWxsik5GSn6ZStsA9x5YM6k3pvV36dRzuvSNVCpFZGQkAM221jfcsh8ZGdmqtUuGjgGIiIhapbpWjh8uZGFzbDJuFKqezD7Eqyf+b3IAJgY68y9jbSASiRAVFaVRfSF19YoYfjTHAERERBqprKnF3vNZ2BKbjJu3K1TaRvjaY83kAIgCHBl82kmTIouaFGuk5ul1AEpLS8PmzZtx/vx5FBYWwtXVFQ899BBWrFgBS8vWlVbPzc3Fli1bcPLkSeTk5MDR0RGTJk3CqlWrYG9v30mfgIhI+2TVtfjuXCY+ik1BdolMpS0kwAFrJvXGqF4OWhqdfmouBDH8dAy9DUAXL17E4sWLUV5ejkGDBiEoKAgXLlzA1q1bERMTg927d8Pa2lqjvjIzMzFv3jzk5+ejT58+mDhxIq5cuYKvvvoKf/zxB/bs2QNXV9dO/kRERF1LVl2L3WcysPVoCvJKK1XaJgQ6Yc2k3hjuw9pRnUVdCNqwYYOybhfA8NMeehmAampq8PLLL6O8vBxvv/025syZAwCQyWR46aWXEB0djY0bN2Lt2rUa9RcWFob8/HysWrUK//d//weg7uiAdevW4ZtvvkF4eDi2bdvWaZ+HiKgrlVfVYNfpDGw7loqCu6rBZ0o/Z6yZ1BuDvbruVHZDdn8IYvjpOHpZjOGXX35BZmYmRo8erQw/AGBubo7169fD0tIS3377LUpKSprppc65c+dw7tw5+Pr6YvXq1crrQqEQ//rXv+Du7o7Y2FgkJyd3ymchIuoqZZU1+Cg2BSJJDN7+NVEl/Ewf4IKf14jwyeJghp8uJhaLGy21sLe3Z/hpJ70MQNHR0QCAqVOnNmqzs7PDyJEjUV1djePHj2vc1+TJkxsdMWFiYoJJkyYBAI4cOdLeYRMRaUWprBqbY5IhkkRDcjAJRWV1BVUFAmBmkBt+e3Estj39AAZ6sFK4NkgkEpWZH6BuJkgikWhpRPpBLx+BXbt2DQAQGBiotj0gIAAxMTFISkrCww8/rFFfffr0abIvAEhKSmrrcImItOKOrBpfnEjHp9I0lFRUK68LBMDDg9yxZlIA+rjYaHGEdP+CZ3t7e2UY0qROEDVNL2eA8vLyAAAuLi5q252dnVXu66q+iIi6g5KKarz/xzWIoqKx8fA1ZfgxEgCPDfXA4ZfG48N5Qxl+tEzdbq/CwkJERUUpr4WFhXEmqI30cgaovLyuMJe5ubna9vrr9fdp0peFhUW7+yIi0qbi8ip8Jk3D5yfSUVpZo7wuNBJg9hB3rJ4YgF5Omu2Opc7V3FZ3TeoEUcv0MgAJhULI5fIWi3FpcmaWUFh3WnFH9EVEpA3F5VX45HgavjiZjrv3BZ/QoR5YNTEAvo5WWhwhNaRJnR+GoPbTywBkZWWF4uJiVFRUqG2XyeoKeTU1q3N/XwA6pC8ioq50u6wKn0hT8eXJGyrBx9hIgMeHeWLVxAB4O7SuKCx1LqlUqnGRQ3UhKCQkhMdhaEgv1wDVr8vJz89X216/Xqf+vq7qi4ioKxSVVUFyMAkiSTQ2x6Qow4+JUIB5I7wR8+oESOYMYvjphkQiEcLDwwFoVudHLBYr1wSFh4cz/LSCXs4ABQYG4tq1a0hOTsawYcMatdfX7Glql9j9fcXExDRZ56c1fRERdabCu5XYfjwVO0/dQHlVrfK6iVCAuQ944YUJ/vC0Y+jp7iIiIlp1qrtYLObMTxvo5QzQ+PHjAQCHDh1q1Hb79m2cOXMGJiYmCAkJ0bivw4cPQy6Xq7RVV1cr6/9MnDixvcMmImqTgruVeOfXRIgkMdh2NFUZfkyFRnh6lA+OvjYRbz8WxPCjQ1obZhh+Wk8vA9DUqVPh7u4OqVSKXbt2Ka/LZDK8+eabKC8vx5w5c+Do6Khsq66uRkpKClJSUlBdfa8exrBhwxAUFISUlBRs3LhRudi5trYWb7/9Nm7duoVx48ahX79+XfcBiYhQF3zW/5qIsZIYbDuWiorqe8Fn8WgfHH19Av796EC49+QaRaL76eUjMHNzc0RFRWH58uVYt24d9u7dC09PT8THxyMvLw/9+/fHq6++qvKa3NxczJgxA0BdVWdPT09l2zvvvIOFCxfi448/xpEjR9C7d28kJiYiIyMDHh4e+M9//tOln4+IDFteqQzbj6biqzM3IKu+NzNtamyE+SO88fx4f7jaqi8DQkR19HIGCABGjhyJ7777DtOnT0d2djZiY2NhY2ODlStXYufOnRqfBA8AvXv3xr59+xAaGorS0lLExMQAAJ5++ml8++23TRZJJN0klUo79X6itsorleHfP1/BuA0x+ESapgw/psZGeGaML46/PhERjwxg+CHSgF7OANXr06cPPvjgA43u9fT0xNWrV5ts9/DwwDvvvNNRQ6NuKiIiApGRkRqfslxfryM8PBwRERGdP0AySHmlMmw7moqvTt9AZc29GR8zYyPMH1k34+PSg6GHqDX0OgARtYZUKkVkZCQAzYqKNSxWFhkZ2apdG0SayLsjw9ajqdh1pnHwWTDSB8+P7wVnBh+iNmEAIvqbSCRCVFSURpVV1VVqZfihjpJ3R4aPjqZg95mMRsFn4SgfrBjH4EPUXgxARA1oUl5ekzL1RG2Re0eGrWqCj7mJERaO9MHy8b3gbMPgQ9QRGICI7tNcCGL4oc6Qe0eGj2JTsDsuA1X3BZ+nR/lg+Th/ONmYaXGERPqHAYhIDXUhaMOGDSgqKlLew/BD7dVc8Fk02hfLxvZi8CHqJAxARE24PwQx/FBHySn5+1EXZ3yItIYBiKgZYrG40cyPvb09ww+1SVPBx8JEiEWjfbBsXC84WjP4EHUFBiCiZkgkEpXwA9TNBEkkEoYg0lhOiQwfxSbj67OZDD5E3QQDEFET7l/wbG9vrwxDmtQJIrpVUoGPYlPwTVwmqmrvBR9LUyGeHu2D5WN7wYHBh0gr9PYoDKL2ULfbq7CwEFFRUcprYWFhkEgk2hgedXPZxRV468e/MH5DLHacuqEMP5amQqwY3wvHX5+INx7qx/BDpEWcASK6T3Nb3TWpE0SGK7u4Altik/Ht2ZuNZnwWj6nb1WVvZarFERJRPQYgogY0qfPDEET3yyquwJaYZHx7LhPVtQrldQYfou6LAYjob1KpVOMih+pCUEhICI/DMDA3b5djS2wKvrsv+Fj9HXyeY/Ah6rYYgIj+JhKJEB4ervFp8A1DUHh4OMOPAcksqgs+359vHHyeCfHFc6JesGPwIerWGICIGoiIiGjVqe5isZgzPwYks6gcm2OS8f35m6iR3ws+1mbGeGaML5aK/Bh8iHQEAxDRfVobZhh+9F9zwWdJSF3w6WnJ4EOkSxiAiIiacKOwDJuik7EvPgu1DYKPzd/B51kGHyKdxQBERHSf9IIyfBidjB//vC/4mBtjSYgflob4wdbSRIsjJKL2YgAiIvpbav5dbPo7+DTIPehhboxnRX5YEuIHWwsGHyJ9wABERAYvOe8uNkVfx/6EbJXgY2thgqUiPzwT4ose5gw+RPqEAYiIDNb13FJ8GJ2MAxezoWgQfHpamuA5kR8Wj/GFDYMPkV5iACIig5OUcwcfRifj10u3VIKPnaUJnhvbC4vH+MLajD8eifQZv+FEZDAuZ5dgU3QyfvsrR+W6vZUplo3thUWjfWDF4ENkEPhNJyK9d+lmCT6Ivo7DV3JVrjtam2LFOH8sGOUNS1P+OCQyJPzGE5Heis+4jQ+jkxGdlKdy3cnGDM+P98f8Ed6wMBVqaXREpE0MQESkd86lF+GD6GQcu5avct21hzlemOCPJ4O9YG7C4ENkyBiAiEhvnE4txAdHruNkSqHKdXdbc7wwMQBzH/CEmTGDDxExABGRjlMoFDiRXBd84tKLVNo87SywemIAQod5wtTYSEsjJKLuiAGIiHSSQqFA7NV8fBB9HfEZxSptPg6WWD0xAI8O9YCJkMGHiBpjACIinSKXK3A4MRebopNxKatEpc3fyQqrJwVg1iB3GDP4EFEzGICISCfUyhX47a9bkBxIQGapXKWtj4s11kzqjRlBbhAaCVTapFIpRCJRVw6ViHQAAxARdWs1tXLsT8jG5phkpOSXqbQNcO+BNZMCMK2/K4zuCz4AIJFIEBYWhvDwcERERHTRiIlIFzAAEVG3VFUjx74LN7ElNgUZReUqbZXZV/Fob3NsWfMCBILGwQe4F34AIDIyElOmTOFMEBEpMQARUbciq67FnrOZ2HY0BdklMpU2N+My/LnrHcjS/8RWAL6mpRCLxY36aBh+ACAqKorhh4hUMAARUbdQVlmDXWduYPuxNBTcrVRpEwU4Ys2kAIzs5QCJTRrCwv4EAGXIaRiC1IUfdSGJiAwbAxARaVVJRTW+PJmOz06kobi8WqVtSj9nrJoYgKHedspr9WGmPuQ0DEEMP0SkKQYgItKKgruV+Eyahh2nbuBuZY3yukAAzBjohpUT/THA3Vbta9WFoA0bNqCo6F4hRIYfImpOqwLQvHnzsHbtWvTr16+zxtNhZDIZduzYgQMHDiAzMxMWFhYIDg7GypUr0bdv31b19corr+Dnn39usn3BggVYu3Zte4dMZBBulVRg29FUfHM2A7Lqe9vZhUYCzB7sjpUT/RHgbNNiP/eHIIYfImqNVgWg+Ph4zJkzB0888QT+8Y9/oGfPnp01rnaprKzEsmXLEBcXBycnJ4wbNw63bt3CoUOHEB0djW3btiEkJETj/i5fvgwAmDlzJoyMGhdXGzRoUIeNnUhf3Sgsw9ajKfj+/E1U1yqU102EAswZ7oUXxvvD28GyVX2KxeJGMz/29vYMP0TUolYFoPnz52PPnj3Ys2cPfvvtN/zjH//AU0891eQ2VG3ZunUr4uLiIBKJsHnzZpibmwMAfvrpJ4jFYrz++uv4/fffYWVl1WJfZWVluHHjBpycnLBx48bOHjqR3knKuYOPYlNwICEb8nu5B+YmRpg/wgfLxvnBzdaiTX1LJBKV8APUzQRJJBKGICJqVqtqxa9duxZ79+7FsGHDUFJSgnXr1iE0NBTnz5/vrPG1Wnl5OXbs2AEjIyOsW7dOGX4AYPbs2ZgxYwYKCgrw448/atRfYmIi5HI5goKCOmvIRHopPuM2nvvyHB58/zh++vNe+LExM8aqif44IZ6EtbP6tyv8NFzwbG9vr/zfYWFhkEgk7Ro/Eem3Vh+W07dvX+zatQsSiQSOjo5ITEzEwoUL8frrryMvL68zxtgqZ8+exd27dzFgwAB4eHg0ap8+fToAIDo6WqP+/vrrLwBgACLSgEKhgPR6AeZtP43HtpzEH4m5yjZ7K1O8Nj0Q0rBJeG16XzhYm7X5fdTt9iosLERUVJTyGkMQETWnzbvAZs+ejSlTpmDTpk3YuXMnDhw4gCNHjmDlypVYvHgxjI21s8Hs6tWrAIA+ffqobQ8ICAAAJCUladTflStXAABCoRAvv/wy4uPjUVhYCC8vL8yaNQtLliyBmVnbf5AT6QO5XIHfr+Tio9hkJNxUPaDUzdYcy8f1wlPB3rAwFbb7vZrb6t7cFnkioobadVyylZUVxGIxfvrpJ4waNQplZWV49913MWvWLEil0o4aY6vUz0K5uLioba+/XlBQALlcrvaehuoXQG/cuBHx8fEYMGAA+vfvj4yMDPzvf//DwoULcffu3Q4aPZFuqa6V4/vzNzHt/WN4/qvzKuHH18ESUaFBOPraRCwJ8ev08FNPLBZzJoiIWtQh0zT+/v74/PPPcejQIUgkEqSlpWHZsmWYNGkSwsLC4OXl1ea+V6xYgdjYWI3uPXLkCMrL684MsrBQv66g4WxNeXk5rK2tm+yvoqICaWlpAOq2wj/33HPKXWCpqalYs2YNLl68iPXr12P9+vUajZFIH1RU1WLP2Qx8fDwNWcUVKm393Hpg1UR/PDSw8cns7SGVSjUucqhuJigkJITHYRCRUoc+p5o0aRJsbW3x5ptvIisrC9HR0ZBKpXjuueewfPnyNj0qcnBwULuWRx1jY2MIhc3/LbPhjjWFQtHMnXUh6uTJkygoKFA+OqvXq1cvSCQSPP744/jxxx8hFotha6u+aBuRvigpr8aOU+n4/GQ6isqqVNqCfe2wckIAJgQ6dcrOUJFIhPDwcERGRmpU56dhCAoPD2f4ISIV7QpAmZmZSEhIwJ9//omLFy8iKSkJ1dX3StkrFApUVlZiy5Yt2L9/P9atW4fRo0e36j1aO7NSv7VdJpOpbW94veEOsab07NmzyXpHAwcOhKurK3JycnDlypVWfzYiXZF7R4ZPjqdi95kMlFXVqrRN6uuMFyb4I9jXvolXd5yIiIhWneouFos580NEarUqAJ04cQIJCQm4ePEiEhISUFxcrGyrn00RCoXo06cPhg0bhqFDh8Lc3BwffPABrl27hqVLl2LlypVYvXp1x36KBurX+OTn56ttz82t25Vib28PExOTdr+fm5sbcnJyUFFR0fLNRDomOe8uth9LwQ/xWSrFC40EwKzB7nh+vD/6ufXo0jG1Nsww/BCROq0KQEuXLoVAIFB5dGRjY4NBgwZh2LBhGDZsGAYPHgxLS9VqrpMmTcKOHTvw7rvvYvPmzXB3d0doaGjHfIL7BAYGAgCuX7+utj05OVnlvuacPn0a33//PTw8PPDSSy+pvefWrVsA6oIQkb6Iz7iNrUdT8PuVXDR8UmxqbIQnH/DCsrG9Wl21mYioO2n1IzBPT0/l7M6wYcPQu3fvFp/3GxkZ4ZlnnoGjoyNeffVV7Nq1q9MC0PDhw2FtbY1Lly4hJycHrq6uKu0HDx4EAEyYMKHFvhQKBQ4cOABLS0ssW7as0YLpU6dOKd9Dk0BF1J0pFArEXs3H1qMpOJOmWl3ZxtwYT4/ywZIQPzjZsOwDEem+Vj8Cc3BwaPObPfzww4iIiEBqamqb+2iJmZkZ5s6di88++wxhYWHYtGmTMrjs378fBw8ehJ2dHebOnavyuuzsbFRUVMDOzk5ZUXbkyJEICAhAcnKy8rTp+tmt69ev44033gAArFmzRu0ZYUS6oLpWjgMJ2dh2NBVXc0tV2pxtzPDcWD/MG+ENG/P2PzImIuouWhWA2hN+6vXo0UP52KizrFmzBnFxcTh16hSmTp2K4OBg5OTkICEhAaampvjf//7X6DGdWCxGXFwcVq9ejTVr1gCom7nauHEjnnnmGRw+fBhTpkzB4MGDUV5ejnPnzqGmpgaLFi3CnDlzOvXzEHWGu5U1+CYuA59J05BdorppoJeTFVaM64VHh3rAzLj99XuIiLqbLi/XHB4ejgsXLnTqe1haWmLnzp34+OOP8euvvyImJgZ2dnaYNm0aVq1ahb59+2rcV2BgIH766Sds27YNsbGxOH78OCwtLTFy5EgsWLAAkydP7sRPQtTx8kpl+OJEOr46fQN3ZDUqbUO9e+L58f6Y2s8FRh1Yw4eIqLsRKFoqhkNdKjQ0FJcvX8aAAQOwb98+bQ+H9Ehy3l18fCwVP8RnoapWtQr65L7OWD6uF0b42XdKDR8ioq7Qmt+h2jmwi4i6hEKhwNn029h+LAV/JKoeVmwiFODRIR5YPq4XervYaGmERETawQBEpIdq5Qoc/CsH24+nIiGzWKXNxswY80d5Y8kYP7jatlwMlIhIHzEAEemRssoafHcuE5+eSENmkWpxTjdbczwb4oenRnhxRxcRGTwGICI9kHtHhi9OpmP3mQyUVFSrtPVz64FlY/0wa7A7TIQs10BEBDAAEem0K9l38Kk0DfsTVI+qAIBxfZywfGwvhAQ4cGEzEdF9GICIdIxcrsDRa/n4RJqKE8mFKm0mQgFmD/HAc2P90Ne1a8/oIiLSJQxARDqioqoW++Jv4jNpGlLyy1TabC1MsGCkNxaP8YVLDy5sJiJqCQMQUTeXUyLDjlPp2B2XgeJy1fU9vg6WWCryw+PDPWFpyq8zEZGm+BOTqJu6dLMEn51Iw4GEbNTIVdf3jPCzx7KxvTCprzOErNhMRNRqDEBE3UhNrRyHr+TisxNpOJt+W6XN2EiAWYPdsVTkh4EetloaIRGRfmAAIuoGSsqr8c3ZDOw4dQNZxar1e3pa1q3vWTSa63uIiDoKAxCRFiXnleLzE+nYdyELFdW1Km29na3xrMgPjw7xgIUpT2QnIupIDEBEXUwuVyD2Wh4+P5GO49cLGrVPCHTCUpEfRAGOrN9DRNRJGICIusgdWTW+P3cTX55Kx43CcpU2S1MhnhjuicVjfNHLyVo7AyQiMiAMQESd7HpuKb48VfeYq7xK9TGXt70lFo32wdxgL/Tg+VxERF2GAYioE9TUynEkKQ87TqU3qtYMAKIARzwzxhcTuY2diEgrGICIOlDh3Up8czYTu07fQHaJTKXN0lSI0GEeWDTaF31cbLQ0QiIiAhiAiNpNoVDgz8xi7Dx1Az9fvIWqWrlKu6+DJRaN9sXjwz1ha8HHXERE3QEDEFEbVVTVYn9CFnaevoG/su6otAkEwMRAZzw92gfjezvBiI+5iIi6FQYgolZKzruL3Wcy8P35TNyR1ai02VqY4MlgLywc6QNvB0stjZCIiFrCAESkgeq/j6jYeeoGTqU2XtQc5GGLp0f74JHB7jA3YdFCIqLujgGIqBk3b5fjm7hM7DmXifzSSpU2M2MjPDzIHYtG+2CwV08tjZCIiNqCAYjoPrVyBWKv5mHXmQzEXM2DQvUgdvg5WmHBSG/MGe6Jnpam2hkkERG1CwMQ0d9ulVRgz9lM7DmbiVv3bWEXGgkwpZ8zFo7yQYi/Ixc1ExHpOAYgMmg1tXIcvZaPr+MyEZ2UC/l9sz3utuZ4aoQ3ngz24knsRER6hAGIDNLN2+X49mwmvj13Ezl3VGd7jP7ewj5vhDcrNRMR6SkGIDIYVTVy/JGYi2/OZuL49fxGa3tce5jjyWAvPBnsBfeeFtoZJBERdQkGINJ7yXl3sedsBvZdyEJhWZVKm9BIgImBzpg/0gvj+3C2h4jIUDAAkV66W1mDXy5mY8/ZTFzIKG7U7mVvgbnDvTCXa3uIiAwSAxDpDYVCgbi0Inx3/iZ+vXQL5VW1Ku2mQiNMG+CCp4K9McbfgTu5iIgMGAMQ6bzs4grsu3AT35+/ifTC8kbtgS42mBvshceGesDeinV7iIiIAYh0VEVVLX6/koPvz9+ENLmg0YJmGzNjPDLEHU8GeyHIwxYCAWd7iIjoHgYg0hkKhQLnb9zG3gs38XPCLZRW1jS6JyTAAU8M98L0Aa6wMOWZXEREpB4DEHV7GYXl2Bd/Ez/EZ+GGmkdcXvYWeHyYJ+YM94SnHU9gJyKiljEAUbdUUl6NXy7dwo/xWYhLL2rUbmUqxIwgN8wZ7olgX3suaCYiolZhAKJuo6pGjtirefghPgtHEvNQVStXaRcIgBB/Rzw+3APTB7jC0pT/+RIRUdvwNwhplVyuwLkbt/FDfBZ+vXQLJRXVje4JcLZG6DAPPDbUA262rNBMRETtZzAB6Nlnn0V8fDzi4+Nb/dqamhrs3bsXe/bsQXp6OoyNjREUFITly5dj5MiRnTBa/aZQKJCUU4qf/szGgYRsZBVXNLrH0doUswa7I3SoJwZ69OAuLiIi6lAGEYAkEglOnDgBS8vWL5BVKBQQi8X4+eefYWtrizFjxqC4uBgnT57EiRMn8Pbbb+Pxxx/vhFHrn4zCchy4mI2f/szCtdy7jdotTISYNsAFjw71wNgARxgLjbQwSiIiMgR6HYDKy8sRGRmJH3/8sc197N27Fz///DP69euHL774Aj179gQAnDp1CitWrEBkZCTGjBkDNze3jhq2Xsm9I8PPF29hf0I2EjIbH0khNBJAFOCIx4Z6YGp/F1iZ6fV/kkRE1E3o5W8bhUKBgwcPYuPGjcjIyICXlxcyMzPb1Ne2bdsAAP/617+U4QcARo8ejcWLF2P79u3YuXMnXn/99Q4Zuz4ouFuJ3/7Kwc8J2YhLL2pUpBAAHvCxwyND3DEjyA2O1mZdP0giIjJoehmAsrKy8I9//APGxsZ49tlnMWfOHMyYMaPV/SQnJyMjIwMODg4YPnx4o/bp06dj+/btOHLkiMEHoKKyKhy6nIOfL2bjVEoh5GpCTz+3Hpg12A2zBrnDy571eoiISHv0MgCZmJggNDQUy5cvh5+fH27evNmmfq5duwYA6N27t9pFuPXXMzIyUFFRAQsLw9qhVFRWhd8v5+CXS7dwMqUQtWpSTy9HKzw82B2PDHZDgLONFkZJRETUmF4GIBcXF7zzzjvt7icvL0/ZnzpmZmbo0aMHSkpKUFBQAC8vr3a/Z3eXX1qJ36/k4LdLOTiVqj70eNtbYuYgNzw8yA393biDi4iIup9uH4BWrFiB2NhYje49cuQIPD09O+y9y8rKAADm5uZN3mNmZqZyrz7KLq7A75dz8NtfOTibXqT28ZannQVmBrlh5iA3Hj5KRETdXrcPQA4ODvDwH4+DpQAAGLdJREFU8NDoXmPjjv04QmHdYZqG+Ms8raAMB//KwcHLOWp3bwF1Z3DNGOiGGUFuGOTJ0ENERLqj2weg9evXa+29raysAAAymazJeyorKwFA59f/KBQKXMoqwaHLOfj9ci6u5zWu0wMAfo5WmBHkiocGumGAOx9vERGRbur2AUib6tf+5Ofnq22vrKzEnTt3IBAI4OTk1JVD6xBVNXKcTi3E4Su5+CMxF7dK1Ae9fm498OAAV0wf6IJAFxuGHiIi0nkMQM0IDAwEAFy/fl1t+/Xr16FQKODt7d2mKtPaUFJejdhreTh8JRdHr+ajtLKm0T0CATDc2w5T+7vgwYGu8HGw0sJIqZ5UKoVIJOq0+4mIDBEDUDN8fHzg6+uL9PR0/PnnnxgyZIhK+8GDBwEAEyZM0MLoNHe7rArfn7+JPxJzce7GbbU7t0yFRhgT4IDpA1wxuZ8znG2aXvhNXSciIgKRkZGIioqCWCxu8X6JRIKwsDCEh4cjIiKi8wdIRKSjGID+lp2djYqKCtjZ2cHe3l55fdGiRVi3bh3eeustfP7553B0dARQdxTGjh07YGJigmeffVZbw9bInK0nkZLfeJearYUJJvV1xtT+LhjXxwnWPIaiW5FKpYiMjAQAhIWFAUCzIag+/ABAZGQkpkyZwpkgIqIm8Dfe38RiMeLi4rB69WqsWbNGeX3evHk4duwYYmNjMX36dIwcORKlpaU4d+4cFAoFoqKiuvU5YHK5AqWye4+5/BytMLmvMyb3c0Gwrx0PHO3GRCIRoqKilKGmuRDUMPwAQFRUFMMPEVEzGIBaYGRkhE2bNuGrr77Cvn37IJVKYW1tjTFjxmDFihUYMWKEtofYLCMjAfasGI2EzGIEedrC38la20OiVqgPO82FIHXhR5PHZUREhswgApCnpyeuXr3a7D07d+5sss3ExARLlizBkiVLOnpoXcLP0Qp+jlzIrKuaC0EMP0REbWMQAYhI16kLQRs2bEBRUZHyHoYfIiLNcQEIkY4Qi8WIiopS/pnhh4io7RiAiHSIWCxW2aUIAPb29gw/REStxABEpEMkEonKzA9QNxMkkUi0NCIiIt3EAESkI+5f8NxwJigsLIwhiIioFRiAiHSAut1ehYWFKmuCGIKIiDTHAETUzTW31f3+hdEMQUREmmEAIurGNKnzwxBERNR6DEBE3ZRUKtW4yKG6ECSVSjt9jEREuooBiKibEolECA8PB6BZnZ+GISg8PJxngRERNYOVoIm6sYiIiFad6i4WixESEsLwQ0TUAs4AEXVzrQ0zDD9ERC1jACIiIiKDwwBEREREBocBiIiIiAwOAxAREREZHAYgIiIiMjgMQERERGRwGICIiIjI4DAAERERkcFhACIiIiKDwwBEREREBocBiIiIiAwOAxAREREZHAYgIiIiMjgMQERERGRwGICIiIjI4DAAERERkcFhACIiIiKDwwBEREREBocBiIiIiAwOAxAREREZHAYgIiIiMjgMQERERGRwGICIiIjI4DAAERERkcFhACIiIiKDwwBEREREBsdY2wPoKs8++yzi4+MRHx/f6te+8sor+Pnnn5tsX7BgAdauXdue4REREVEXMogAJJFIcOLECVhaWv7/9u41qIrzjuP4DxFvaSolVjFgpxpdqqBYk6lNxSaK2jZqoyadptEgaRHaKklM7ABjvMDUC6QlKd7CtHGsxhqjqaS8oJhEaUNMUqtGa7SooFEUL1xsNQcIl+0LyolERC7LubDfzwwv3Gd5+O9/znF/5zl79rTr9z/++GNJ0tSpU9Wt282LZqNGjepQfQAAwLW6dAByOBxKTk5WVlZWu+f49NNP9cknn+irX/2q0tPTLawOAAC4S5e8Bsg0TeXk5Ojhhx9WVlaWBg0a1O65jh8/rvr6eo0cOdLCCgEAgDt1yQB0/vx5PfPMM7pw4YJ++tOfKjMzs91zHT16VJIIQAAAdCFd8i0wPz8/zZo1S7GxsRo8eLCKi4vbPdexY8ckSb6+vnr22Wd16NAhlZWVadCgQZo+fbqefPJJ9ezZ06rSAQCAC3TJFaABAwZo1apVGjx4cIfnarwAOj09XYcOHVJoaKhGjBihs2fP6sUXX9ScOXN0/fr1Dv8dAADgOh6/AhQXF6e8vLxW7fvOO+8oODjYsr9dWVmp06dPS2r4KHxMTIzzU2BFRUWKj4/XkSNHtHLlSq1cudKyvwsAADqXxwegu+66S0FBQa3at3t3aw+nd+/e2rdvn0pLSzV06NAmY0OGDFFqaqoeeeQRZWVlKSEhQX379rX07wMAgM7h8QHI3Ssr/v7+8vf3b3YsLCxMgYGBunjxoo4dO6b777/fxdUBAID26JLXALnSwIEDJTW8XQYAALyDx68AudMHH3ygnTt3KigoSAsXLmx2n5KSEkmfByEAAOD5WAFqgWmays7O1ubNm5v9pNf777+vixcvKjAwUCEhIW6oEAAAtAcB6P8uXLigwsJClZeXO7eNHTtWQ4cOlcPhUGJiohwOh3Ps5MmTSkpKkiTFx8c3+x1hAADAM/EW2P8lJCToH//4hxYsWKD4+HhJUrdu3ZSenq7o6Gi99dZbmjRpksLDw+VwOPTPf/5TtbW1ioqK0qOPPurm6gEAQFsQgG4jJCREb775pjIzM5WXl6d3331Xffr00dixYzV79mxFRka6u0QAANBGtghAwcHBKigoaHGfLVu23HKsf//+WrJkiZYsWWJ1aQAAwA24cAUAANgOAQgAANgOAQgAANgOAQgAANgOAQgAANgOAQgAANgOAQgAANgOAQgAANgOAQjwYPn5+Z26PwDYFQEI8FDLly/X+PHjlZqa2qr9U1NTNX78eC1fvrxzCwOALoAABHig/Px8JScnS5ISExNvG4JSU1OVmJgoSUpOTmYlCABugwAEeKCIiAitXr3a+e+WQtCN4UeSVq9erYiIiE6vEQC8GQEI8FAJCQm3DUHNhZ+EhASX1QgA3ooABHiwlkIQ4QcA2q+7uwsA0LLGUNMYdhITE5WWlqby8nLnPoQfAGgbVoAAL/DFlSDCDwB0DAEI8BIJCQkKCAhosi0gIIDwAwDtQAACvERqamqTlR+pYSWotfcJAgB8jgAEeIEvXvB840pQa+4TBABoigAEeLjmPu1VVlbW6vsEAQBuRgACPFhLH3VvzX2CAADNIwABHqo19/khBAFA+xCAAA+Un5/f6pscNheC+C4wAGgZAQjwQBEREVq2bJmk1t3n58YQtGzZMr4LDABugztBAx5q+fLlmjRpUqvDTEJCgsaNG0f4AYBWYAUI8GBtDTOEHwBoHQIQAACwHQIQAACwHQIQAACwHS6C9jDFxcWSpMLCQs2aNcvN1QAA4D0KCwslfX4ubQkByMNUV1dLkqqqqvTxxx+7uRoAALxP47m0JQQgDxMQEKDy8nL17NlTwcHB7i4HAACvUVxcrOrq6iZfGH0rPqZpmi6oCQAAwGNwETQAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALAdAhAAALCd7u4uAG13+vRprVu3TgcOHFBZWZkCAwP1gx/8QHFxcerTp0+b5rp06ZLWr1+vffv26eLFi+rXr58mTpyo+fPnKyAgoJOOwPNY2dO8vDy9+uqrOnr0qK5duyZ/f3+NGTNGMTExCg8P76Qj8CxW9vOLUlNTtXHjRi1YsEDx8fEWVez5rOypw+HQxo0blZubq7Nnz6pbt24aPny4oqKi9P3vf7+TjsDzWNnTjz76SJmZmTp48KA+/fRT3XXXXfrOd76jX/ziF/ra177WSUfg2c6cOaMZM2Zo1qxZWrp0aZt+1xXnJh/TNE1LZoJLHDlyRHPnzpXD4dCoUaM0cOBAHTx4UFeuXFFISIj+9Kc/6Utf+lKr5jp37px+8pOf6MqVKzIMQ4MHD9axY8d07tw5BQYGavv27QoMDOzkI3I/K3uanp6uzMxM+fj4KDQ0VIGBgSoqKlJRUZF8fX21YsUKzZw5s5OPyL2s7OcXvffee/rZz34m0zRtFYCs7Glpaanmzp2rU6dOqV+/fho9erTKysr00UcfyTRNJSUlKTo6unMPyANY2dOcnBw999xzqqurU2hoqO6++24VFBTo7NmzuuOOO7Rp0yaNGjWqk4/Is5SWlioqKkqFhYWaPXt2mwKQy85NJrxGTU2NGRkZaRqGYe7YscO5vbKy0vz5z39uGoZhJicnt3q+xx9/3DQMw/zd737n3FZbW2suXbrUNAzDjI2NtbR+T2RlT/fv328ahmGGh4ebH3zwQZOxbdu2mYZhmGFhYeb58+ctPQZPYvVj9EZlZWXmuHHjTMMwTMMwzIyMDKvK9mhW9zQ2NtY0DMOMj483q6qqnNvfe+89MzQ01Bw+fHiXfoyaprU9dTgc5n333WeGhISY2dnZzu21tbXmypUrTcMwzGnTpll+DJ7s2LFj5uTJk53P1bY+5111biIAeZGsrCzTMAxz7ty5N42Vl5ebo0ePNkNDQ82rV6/edq7Gk/WUKVPMurq6JmOfffaZ+eCDD5qGYZgnT560qnyPZGVPExISTMMwzDVr1jQ7Pm/ePNMwDHPjxo0dLdtjWdnPL4qLizNHjBhhPvbYY7YKQFb29PDhw6ZhGOakSZOahJ9GS5YsMSdMmGDm5uZaUbrHsrKn+/btu2XIqaysNIcPH24ahmGWlZVZUbpHu3r1qpmWlmaGhYWZhmGYEydObHMAcuW5iYugvciePXskSZMnT75p7Ctf+YrGjh2rmpoavfvuu62eKzIyUt26NX0Y+Pn5aeLEiZKkd955p6NlezQre9qrVy8ZhqFvf/vbzY4PGTJEUsN7212Vlf280datW7V3717Nnz9fYWFhltTqLazsaU5OjiTpiSeeUM+ePW8aT0lJ0Z49ezRlypQOVu3ZrOypr6+vJKm8vFyfffZZk7GKigrV1dXJz8+v3W/7epPNmzfrD3/4gwICArRhwwbNmDGjzXO48txEAPIiJ06ckCSFhIQ0Oz506FBJ0r///e9Wz2UYRofn8mZW9nT58uXKzs7Wfffd1+z44cOHJalLX1dlZT8bnTx5UqmpqRozZozi4uI6XqSXsbKnR48elSSNHj1aDodDu3btUkpKipYtW6adO3eqqqrKoqo9m5U9HTlypAICAlRaWqrnnntORUVFqqqq0uHDhzV//nxJUnR0tHr06GFR9Z4rMDBQCQkJys3NdQaVtnLluYlPgXmRy5cvS5IGDBjQ7Hj//v2b7OequbyZq/qwZ88eHTx4UH5+fs2+6uwqrO5ndXW1nn32Wfn5+emFF15wvtq2Eyt7eubMGUkNKxPTpk3T+fPnnWOvvfaaNmzYoJdfflnDhg3rYNWezcqe9u7dW2vXrtXChQu1e/du7d692znWq1cvpaSk6Mc//rEFVXu+H/3oRx2ew5XnJlaAvIjD4ZDU8KRqTuP2xv1aM1fv3r07PJc3s7Knt1JQUKCkpCRJUkxMjIKCgto9l6ezup9paWk6ceKElixZouDgYGuK9DJW9vT69euSpEWLFunOO+/Uq6++qgMHDujNN9/U+PHjVVxcrHnz5jn366qsfpwOHjxYP/zhD+Xr66vQ0FBFRkZq0KBBqqqq0qZNm/Svf/3LmsJtwJXnJlaAvIivr6/q6+vl4+PT4n5mK+5s0PhK2oq5vJmVPW3OkSNHFBsbq6tXr2rChAl66qmn2jWPt7Cyn433U3rooYfadS1BV2FlT6urqyVJPXr00ObNm9W3b19J0je+8Q29/PLLmjlzpk6cOKHXXntNMTExHS/eQ1nZ05KSEs2ZM0cVFRV65ZVXdP/99zt/949//KNWrVqlJ598UtnZ2Ro4cKAl9Xdlrjw3sQLkRe644w5JUmVlZbPjje/f3yo5d9Zc3qwz+/DXv/5VUVFRqqio0KRJk5SRkXHTRX1djVX9LC0tVVJSkgYOHKjk5GRri/QyVj5GG189z5gxwxl+GnXv3l2PPfaYJOn9999vd73ewMqevvjiiyouLtZTTz3lDD9Swwk8Ojpa06dP17Vr17Rp06aOF24Drjw3de3/jbuYxvc+r1y50ux443uijfu5ai5v1ll9WLdunZ555hlVVlbq8ccfV0ZGhi0ugrSqn+vXr1d5ebn8/f2VkpKiRYsWOX/y8/MlSbt379aiRYu0YcMGC4/A81j5GO3Xr58k3fLtxMbtFRUVba7Tm1jZ03379kmSxo8f3+z4gw8+KOnzC9DRMleemwhAXqTxEwunTp1qdrxx+60+2dBZc3kzq/tQX1+vxMRE52rP4sWLtWzZMttcvGtVPxvf3z9+/Liys7Ob/BQVFUlq+LRIdna28wTUVXXG8/5Wt2JoPOl09a/BsbKn//nPfyQ1rKA1p/G5X1tb2+Y67ciV5yYCkBd54IEHJEm5ubk3jVVUVOjDDz+Un5+fxo0b1+q53nrrLdXX1zcZq6mpcd5jYcKECR0t26NZ2VNJev7557Vr1y716dNHGzZsUFRUlKX1ejqr+rl69WoVFBQ0+9PY0wULFqigoEBbtmyx/kA8iJWP0cbViJycHNXU1Nw0/ve//12S9K1vfasDFXs+K3t6zz33SPr8/jVf1LhiOXz48PaWayuuPDcRgLzI5MmTdffddys/P19bt251bq+qqtLixYvlcDj06KOPOpe5pYYHTGFhoQoLC5v8hzdmzBiNHDlShYWFSk9Pd15QVldXpxUrVqikpETf/e53u/yT1sqeZmVl6Y033lD37t21fv165xPZTqzsJxpY2dOHHnpIwcHBOnPmjFJSUpqM7dixQ7m5uerbt68eeeQR1xycm1jZ09mzZ0uS1q5dq/379zf5Ozt37tQbb7whPz8/zZkzp5OPyrt4wrmJL0P1Mh9++KFiY2NVVVWl0NBQBQcH69ChQ7p8+bJGjBihLVu2NLnjaHFxsSIjIyU13Dnzxvf+T548qTlz5ujq1asaMmSIhg0bpuPHj+vs2bMKCgrStm3bbnkvhq7Eip7W1dUpMjJSJSUlGjBgQIuvoCMiIrr0p5qsfIw2Z8WKFdq8ebOtvgzVyp4ePXpUMTExqqioUP/+/RUeHq5PPvlEJ06cUM+ePfXSSy+1+yZ23sTKni5dulTbt2+X1HBjxMDAQJ06dUqnT5+Wn5+fVqxYoYcffti1B+gB1qxZo7Vr1zb7ZaiecG5iBcjLjB07Vjt27ND3vvc9XbhwQXl5ebrzzjv1y1/+8qYn7O0MGzZMf/7znzVr1ixdu3ZNe/fuldRwm/zXX3/dFuFHsqanBQUFKikpkdRwfcUXr1u58efIkSOdfUhuZeVjFA2s7GlYWJiys7P1xBNPqEePHsrLy1NFRYWmTp2q119/3RbhR7K2pykpKVq3bp0iIiJ07tw57d27V9evX9e0adO0Y8cOW4afjnDVuYkVIAAAYDusAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAEAANshAAHALRw4cEAhISEKCQlRTk5Os/scPnxY3/zmNxUSEqK0tDQXVwigvQhAAHAL9957ryZOnChJysjIUF1dXZPxoqIixcXFyeFwaObMmfrVr37ljjIBtAMBCABasGjRIvn6+qqoqEh/+ctfnNsvXbqkmJgYVVRUaMKECfr1r38tHx8fN1YKoC0IQADQgnvuuUczZ86UJK1du1Y1NTX673//q5iYGJ0/f1733nuvXnrpJXXv3t3NlQJoCx/TNE13FwEAnuzSpUuaMmWKqqqqlJSUpLffflv79++XYRjaunWrvvzlL7u7RABtRAACgFb4zW9+o9///vfOfwcFBWnbtm0aMGCAG6sC0F4EIABohcuXL+uBBx5QfX29/P39tX37dn396193d1kA2olrgADgNmpra7V06VLV19dLkiorK9WrVy83VwWgIwhAANAC0zT1/PPPa+/evQoICFBwcLCqq6uVkZHh7tIAdAABCABakJaWpl27dqlPnz7KzMzUwoULJUlZWVk6deqUm6sD0F4EIAC4hVdeeUUbN26Un5+f1qxZo1GjRmnq1KkKCQlRXV2dfvvb37q7RADtRAACgGZkZWXphRdekI+Pj1atWqWIiAhJko+Pj55++mlJ0p49e3TgwAF3lgmgnQhAAPAFf/vb37R48WKZpqnExERNnz69yXhkZKTCw8MlNXw8HoD3IQABwA0OHTqkp59+WrW1tZo3b56io6Ob3a/xWqCDBw/q7bffdmGFAKzAfYAAAIDtsAIEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABshwAEAABs53/dO2trjI500gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First the mean on some test points\n",
    "x_star = np.linspace(0, 1, 100)[:, None] # This is needed to turn the array into a column vector\n",
    "m_star, v_star = gpm.predict(x_star)\n",
    "# Let's plot the mean first\n",
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data')\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extracting the variance is a bit more involved.\n",
    "Just a tiny bit though.\n",
    "This is because ``v_star`` returned by ``gpm.predict`` is not exactly $\\sigma_n^2(x)$.\n",
    "It is actually $\\sigma_n^2(x) + \\sigma^2$ and not just $\\sigma_n^2(x)$.\n",
    "Here, see it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/V8eOHVGr1Vy4cEH/t+BRe/fuZf78+VhZWbFy5Ur9IujJkydjbGzM/v37uXTpUq5tJyQkEBQUhKWlJe3aKb9TwtN8riVZmUqUsqe8cisCGRsby6lTpzAxMSl0xc9PPvmE7du3Y2lpyQ8//ICHh0ee1wYGBub5U7FiRQAOHTpEYGAg7u7uRXh3JdOYzo30o0pbfMMIjZFRJSFEyebh4UHTpk1JTU1lxIgRvPzyy7z66qt07dqVvXv3Ym9vz7p16x6rfZSWlsaNGzc4efIk27dv5+233+b7778H4IMPPsi1rxo1auDq6sqDBw/0tYKyHT9+nBkzZmBsbMyyZcv003QAdevWxd3dHa1Wy8KFC3Nt+48//iAjI4O+ffvql54oqaifa0lXphKlnj17UqdOHY4dO8avv/6qP56amsqsWbNITk5m0KBB2NjY6M9lZGQQEhJCSEhIjmx/x44deHt7Y2xszPLly8vFuqOiqGxpwluddWuVMrO0LPW5pnBEQgiRPysrKzZs2MBbb71FvXr1CAsLIzQ0lBYtWvDpp5+ybdu2XBckBwYGotFoaNasGatXr6ZXr164ubkxcuRIIiMjSUxMzLW/7FIxu3bt0h+7cuUKkyZNIjMzk7lz59KxY8fH7nv33XcxNTXl+PHjnDhx4rHz2e3lVrFbCUX9XEu6MvXUm7m5OfPnz2f8+PF88cUXeHt7Y2dnh5+fH5GRkTg6OjJ9+vQc90RERNCnTx9AN+JjZ2eHRqPRzwtXq1YNb29vvL29c+2zc+fODBw48Nm+sRLurc4NWfPPDR6kZuJ97g7vutrTQOoqCSFKsIoVKzJjxgxmzJhR6HsCAgIAmDp1ao7jsbGxWFhY5Dmq07VrV5ycnDh06BChoaHUrVsXR0dHzp07l29/tWvX5uLFi7meu3z5MqdPn8bV1TXf7VEKy93d3SCzHUX5XEu6MpUoAbi4uLBlyxaWLVvG6dOnCQ4Oxs7OjkGDBjFmzBgqVKhQYBuBgYH6qqERERH5bmxbqVKlcp8oVbYwYWyXRiw6GIQmS8tSn2AWvi51lYQQZUtAQAC1atV6rKbQlStXaNq0ab6laWbMmMHw4cNZvnw58+bNe+pYli5dilqt5sMPP3zqtkT+ylyiBLrCWEuWLCnUtXZ2dgQGBuY45ujo+Nixp1FWnnLLz+hODVh97MbDukphTHRrTKPqBSelQghRWgQEBOT6GH5AQECBa1/btm3LnDlziIuLQ6PRPNUeoCkpKTz//PO89NJLperpsdKqTK1REsqpaG7C+IeVc7O0sOSQrFUSQpQdWVlZBAUF5VhwDZCYmEhoaGih6hgNGzaMd95556k3SrewsGDSpEnlfjajuEiiJAxmZMcGVLE0AWDnhXCCIxMUjkgIIQzjxo0bJCcn8/zzz+c4HhAQgFarfSyBEmWHJErCYCqYGTO+q24YWKuFxQdlVEkIUTZcvXoV4LGE6MqVK5iYmNCkSRMlwhLFQBIlYVAjO9bHpoJuE8e9F+9y6U7BG0EKIURJ17dvXwIDAx/b2WHkyJFcunTpsd0aRNkhiZIwKEtTYya5/bu4cMEBwy2KF0IIIYqbJErC4Ia51MPWWrfx8F+BUZy+EaNwREIIIUTRSKIkDM7MWM3UHv/O13+7/yparVbBiIQQQoiikURJPBPurW1pVF1XpfbMzViOBEUpHJEQQgjx5CRREs+EsdqI93s66F8vOBAoo0pCCCFKHUmUxDPz8vO1cKxdCYBLdx6w79I9hSMSQgghnowkSuKZMTJS8UHvR0aV9geSqclSMCIhhBDiyUiiJJ4pV4fqODeoCsD1+0n85huqcERCCCFE4UmiJJ4plUrFjJeb6V9/9+c1ktMzFYxICCGEKDxJlMQz17Z+FV5qXguAqIQ0fjp2Q+GIhBBCiMKRREkUiw9eckBtpALA68h1ohPTFI5ICCGEKJgkSqJYNK5egSEv1AUgMS2TZYeDFY5ICCGEKJgkSqLY/K97EyxM1AD8cvIWt6OTFY5ICCGEyJ8kSqLY1KhkztguDQHI0Ghlw1whRKmzf/9+pk6dyosvvkjLli3p1asXX331FbGxsUqHJp4RSZREsRrftRFVrUwB2HUhnPOhcQpHJIQQhbd69Wo0Gg1Tpkxh1apVjB49mn379jF06FBSUlKUDk88A8ZKByDKl4rmJkzt3oTZuy4D8PXeK2ye0AGVSqVwZEIIUTAvLy+qVq2qf+3s7EyDBg0YNWoU+/fvZ+DAgQpGJ54FGVESxW64Sz0a2fy7Ye7+y7K1iRCidHg0ScrWokULACIiIoo7HFEMJFESxc5EbcRHjxShnL/vKumZsrWJEKJ0OnnyJACNGzdWOBLxLEiiJBTR07EmLg1138xuRiez/uQthSMSQognFx8fz7x582jatClubm5KhyOeAUmUhCJUKhWf9HXUv15y6BpxyekKRiSEEE8mLS2NSZMm8eDBAxYvXoxarVY6JPEMSKIkFNPCrjLurW0BiE/JYMkhKUIphCgdMjIymDJlChcvXsTLywt7e3ulQxLPiDz1JhQ1vbcDey/eJS0zi/Unb/Jm+3o0ql5B6bCEEOXEvXv3+Pnnnzl27BhhYWEkJSXlep2xsTF+fn6Ympqi0Wh4//33OX78OF5eXrRt27aYoxbFSUaUhKLqWFswvmsjQFeE8uu9AQpHJIQoL06cOEH//v1ZvXo1169fp169ejRp0iTXciUNGzbE1NSUrKwsZsyYwaFDh1i8eDGdOnVSIHJRnGRESSju7W6N2ewbSsSDNA5djeSvwEhcHWooHZYQogy7ceMGEydOJCkpiX79+jFr1iz9o/9Xr17Fw8OD+Ph4BgwYwFtvvUWFCrqR7i+//JLdu3czcuRIbGxsOH/+vL7NWrVqUatWLUXej3h2ZERJKM7KzDhHuYAv91whQyPlAoQQz85XX31FUlISzs7OLFiwIEd9pGbNmjFixAgAAgMDee6556hbV7ep95EjRwBYt24dQ4YMyfGzZcuW4n8j4pmTESVRIrziZMvPJ27hdzuOkKgk1p+4xVudGyodlhBly6JFup+CtGkDu3blPDZgAJw7V/C906bpfrIlJMBzzxUuvp074dH1Pnv2wNtvP97mU7p27RrHjh3DyMiIuXPn5jrV5uTkBMDdu3dzHPfx8TFYHKJ0kERJlAhGRipm92/OQM9/AFj8ZxCvtKpDtQpmCkcmRBny4AHcuVPwdQ9HT3KIiircvQ8e5Hyt1RbuPoD0/5QISUnR3fvfNp/SwYMHAWjbtq1+pOi/sh/1NzU1NWjfovSRREmUGK3qWjOorR1bz4aRkJrJooNBfP1qC6XDEqLsqFQJbG0Lvq569dyPFebeSpVyvlapCncfwH+TEgsL3b3/bfMp+fn5AdC1a9c8r7l58yYA9evXN2jfovSRREmUKB/2dmDfxbskpWvYePo2b7jUx7GOYf+RFKLcepoprP9OxRVWxYoQFla0e/v1K/q9+bh9+zaQfxKUPcXm7Oxs8P5F6SKLuUWJUqOSOZNebAJAlhZm77qEVqtVOCohRFmS/nCKT6PR5Hr+zp07nDp1CoD+/fsXW1yiZJJESZQ4b3VuQEMbKwDO3Ixlu18h1zcIIUQh1KihKz9y4cKFx85ptVpmzZpFRkYGvXv3lo1uhSRKouQxM1Yzu/+/+8DN/f0qD1IzFIxICFGWuLq6ArBp0yZOnz6tPx4TE8P777/PiRMnqF27Np9++qlCEYqSRNYoiRLJ1aEGvZvXZP/lCO4nprH4YBCz+zdXOiwhRBng4eHB77//TlBQECNGjKBRo0aYm5tz7do1MjIysLe3Z/ny5VTPbVG7KHdkREmUWJ/2c8TcRPcr+vOJW1y9Z9hHhIUQ5ZOVlRUbNmzgrbfeol69eoSFhREaGkqLFi349NNP2bZtmzztJvRkREmUWHZVLJnkZs+CA0FosrR8tuMyv01on2txOCGEeBIVK1ZkxowZzJgxQ+lQRAknI0qiRBvXtRENqlkCcPpmDDvOy8JuIYQQxUcSJVGimRmrmTPg37VJX+8NID5ZFnYLIYQoHpIoiRLP1aEGLzXX7ch9PzGdb/ZfVTgiIYQQ5YUkSqJUmD3AEStT3d5LG07d5uytWIUjEkIIUR5IoiRKhdqVLXi/l4P+9aztF8nQZCkYkRBCiPJAEiVRanh0qE/zh/u+Xb2XwE/HbigckRBCiLJOEiVRahirjZj7aguyqwN89+c1wmKTlQ1KCCFEmVYm6yjduHEDT09Pzp49S3R0NLVq1eLll19mwoQJWFpaPlFbf/31F7/88guXLl0iISEBa2tr2rRpw9ixY3Fycnrs+pSUFNasWcP+/fu5desWWVlZ2Nra0r17d8aOHYu1tbWh3ma55FTXGo/29Vl34hYpGRo+23mZ1SPbSW0lIYQQz0SZG1Hy9/fH3d2d3bt3Y2Njg6urK8nJyXh5eTF06FASExML3daiRYuYMGECx44dw9bWFldXVypVqsSBAwcYNmwY27dvz3F9XFwcr7/+Ot9//z137tyhdevWODs7ExMTw48//oi7uzv37t0z9Fsud97v7UCNimYA+FyNZI//XYUjEkI5j35JyMqSdXuifHr0d9/QX5zLVKKUmZnJtGnTSE5O5uuvv2bLli0sWbKEP//8kxdffJHAwEAWLVpUqLZ8fX1ZsWIFFhYWrFu3Dm9vbzw9Pdm3bx+ff/45Go2Gzz77jPDwcP093377LUFBQTg7O3PgwAHWrFnDqlWrOHjwIF26dOHOnTuyyaIBVDI34YtX/q2tNGfXZWKT0hWMSAjlqFQqTE1NAUhKSlI4GiGUkf27b2pqKolSfvbu3UtoaCgdOnRg0KBB+uPm5ubMnTsXS0tLNm/eTHx8fIFtbd26FYCxY8fi4uKS49zQoUPp1q0b6enp7N+/H4DU1FT27NkDwPz586latar++kqVKvHNN9+gUqk4evQosbHyaPvTeun52vRuXhOA6KR0vtx7ReGIhFBOxYoVAYiIiCA+Pp7MzEyysrLkR37K/E9mZibx8fFERETk+G/BkMrUGiUfHx8Aevbs+di5KlWq4OLiwuHDhzl69Cj9+vXLty1zc3OaNm1K+/btcz3fqFEjjhw5ov8/Jzo6mubNm6PVarG1tX3s+mrVqlG5cmXi4uKIjIykSpUqT/r2xH988crzHA+JJiE1k23n7jCwlS1dm8pu36L8qVatGklJSaSmpuYY5RaiPDE3N6datWoGb7dMjSgFBQUB4ODgkOt5e3t7AK5eLbiy85w5c9i9ezft2rXL9fyFCxcAqFVLVzHa1taWDRs2sHHjxlyvv3XrFnFxcRgZGVGzZs0C+xcFq1nJnFl9ntO//nj7RZLSMhWMSAhlqNVq6tWrR7Vq1fTTcEKUF6amplSrVo169eqhVqsN3n6ZGlGKjIwEyDMRqVGjRo7risrHx4dz585hYmKS6+hVbhYsWABAx44d5ck3AxryQl12ng/nxPVowmJTWHggiM/6OyodlhDFTq1WU6NGDWrUqIFWq0Wr1SodkhDPnEqleuZPPZepRCk5WVdTx9zcPNfz2cezryuKwMBAZs6cCejWL+U2zfZfXl5eHDhwAHNzcz788MMi9y0ep1KpmOfegt7f/U1aZhZrjt+gb8vatK0vU5ui/CqOPx5ClBdlauote8itoH8givpNy9/fn5EjRxIXF4ebmxtTpkwp8J4lS5awePFijIyMmDt3bp7TgqLoGthYMa1nUwC0Wvhg6wVSMzQKRyWEEKIsKFOJkpWVFaAr+pib1NRUACwsLJ647T/++AMPDw9iY2Pp0aMHS5Yswcgo748vPT2dDz/8EE9PT4yNjfnmm2/o27fvE/crCmdM54Y41dVNaV6PSmLRwSCFIxJCCFEWlKlEKXsNUlRUVK7ns9cmZV9XWJ6envzvf/8jJSWF4cOHs2TJknwXTEZHR+Ph4cHOnTupUKECK1asYMCAAU/Up3gyxmojFg5uiamx7lf6x6PXOXtLyjAIIYR4OmUqUcqe1goODs71fPbxwk5/ZWVl8dFHH+lHj2bNmsXs2bPzXVV/+/ZtBg8ejJ+fH3Z2dmzatInOnTs/4TsRRWFfo2LOKbgtMgUnhBDi6ZSpRKlbt24A+iKQj4qNjeXUqVOYmERQUQAAACAASURBVJjQqVOnQrX3ySefsH37diwtLfnhhx/w8PDI9/qIiAg8PDy4c+cOLVu2ZPPmzTRp0uTJ34gosnFdGtEqewrufhILDwQqHJEQQojSrEwlSj179qROnTocO3aMX3/9VX88NTWVWbNmkZyczKBBg7CxsdGfy8jIICQkhJCQEDIyMvTHd+zYgbe3N8bGxixfvlyfhOXngw8+4O7duzg4OLB27dpnUvhK5E9tpGLBI1Nwq47dwPdmjMJRCSGEKK3KVHkAc3Nz5s+fz/jx4/niiy/w9vbGzs4OPz8/IiMjcXR0ZPr06TnuiYiIoE+fPgAcOnQIOzs7NBoN3333HaCreOvt7Y23t3eufXbu3JmBAwfyzz//cOrUKUBXQn327Nl5xjl16lTq1q1riLcscpE9BTd/31W0Wpi2+QL7pnbByqxM/boLIYQoBmXuL4eLiwtbtmxh2bJlnD59muDgYOzs7Bg0aBBjxoyhQoUKBbYRGBjI3bu6HekjIiLYvXt3ntdWqlSJgQMHcvjwYf0xX1/ffNsfOXKkJErP2LgujTh4JYKzt2K5HZPMV3uvMM+9pdJhCSGEKGVUWinfWmq5u7tz+fJlmjdvzrZt25QOp8S5FZ3Ey98fJTldt6B79ch2dH9Oto8RQghR+L+hZWqNkhCPql/Nik/6/rudyQxvf6IT0xSMSAghRGkjiZIo04Y51+XFZrq6WfcT05m57aLsgSWEEKLQJFESZZpKpWL+ay2oYmkCwIErEWw5G6ZwVEIIIUoLSZREmVejojnz3FvoX3++6zI37ycpGJEQQojSQhIlUS689HxtBre1AyApXcPUTX5kaLIUjkoIIURJJ4mSKDfmDGhOQxvdxskXwuJZLBvnCiGEKIAkSqLcsDIz5vuhrTBRqwD44UgIx4PvKxyVEEKIkkwSJVGutLSzZnov3abIWi28t/k8sUnpCkclhBCipJJESZQ747o0opO9bh++iAdpfOjtLyUDhBBC5EoSJVHuGBmpWPR6K33JgINXIlh7/KayQQkhhCiRJFES5VLNSuYsfN1J/3ru7wH4h8UpGJEQQoiSSBIlUW692Kwm47s2AiBDo2XihnPEp2QoHJUQQoiSxNjQDd64cYPz588TGRlJTEwMaWlpWFtbU7VqVRo3bkybNm2wsLAwdLdCFMkHvR04czMGv9txhMak8JG3P8vfaINKpVI6NCGEECWAQRIlPz8/Nm/ezNGjR4mOjs73WrVaTfPmzenfvz+vvPIKFStWNEQIQhSJidqIpcNa03fJMeJTMth36R7rT97Co0MDpUMTQghRAjxVorRz505WrVpFcHBwjqeGLC0tsba2xtraGjMzM+Lj44mPjyc2NpbMzEwuXLiAv78/CxcupG/fvkycOJHatWs/9ZsRoijsqliyYLAT4372BeCrPQE42VnjVNda4ciEEEIorUiJ0qlTp/jmm28ICAhAq9VSuXJlevfuTbt27XBycqJ+/fq53peUlMSlS5e4cOECPj4+nD9/nq1bt7J79248PDyYMGECFSpUeKo3JERR9HSsydjODVl17Abpmize/fUcuyd3pqqVqdKhCSGEUFCREqWRI0cC0LlzZ4YOHUq3bt0wMTEp8D4rKytcXFxwcXFh/PjxhIWFsWPHDn755RdWrVqFubk5EydOLEpIQjy1D19qhl9oHGdvxXInLoWpm/xYO9oZtZGsVxJCiPKqSE+9de7cmd9++41Vq1bRo0ePQiVJubGzs2PSpEkcPnyYadOmYW0tUx1COabGRngOb4NNBd0o0tFr9/n+T9kPTgghyrMijSitWrXKoEFYWFgwbtw4g7YpRFHUqmzO0mFteHP1KTRZWpb4BONU15ruz9VUOjQhhBAKkDpKQvxHh8bV+LC3g/71e7+d51Z0koIRCSGEUIrBEqUFCxYYqikhFDe+ayNeal4LgAepmYz/+SxJaZkKRyWEEKK4GSxRWrVqFR9//DFZWVmGalIIxahUKr4d3JJG1a0ACIxIYPqWC7J5rhBClDMGS5QsLCzYvn07kyZNIj09vVD3+Pj4GKp7IQyuorkJP3q0o6KZbinfvkv3WOYTrHBUQgghipPBEqW1a9dSuXJlDh8+zJgxY0hMTMzzWj8/P9544w0mTZpkqO6FeCYaV6/AkmGtyd7RZOHBIA5eiVA2KCGEEMXGYImSk5MTGzZsoHbt2vj6+vLmm28SFRWV45qQkBAmTpzI8OHDOXv2rExjiFLBrVkNpvfKubg7ODJBwYiEEEIUF4M+9daoUSM2btyIvb09V69eZfjw4YSGhhIREcEnn3zCK6+8go+PD1qtFicnJ3766SdDdi/EM/Oua2P6tdRts5OYlsmYdb7EJhVuilkIIUTpZZBNcR9Vs2ZNfv31V9599118fX0ZPHgwqamppKWlodVqcXBwYOrUqbz44ouG7lqIZ0alUvF/g1pyPSqJK3cfcCs6mQm/nOWXMS6YGkuVDSGEKKueyb/wVlZW9OzZE4D4+HhSU1Oxs7Nj4cKF7Ny5U5IkUSpZmhrz48h22FQwA+D0jRg+2XFRppCFEKIMM2iipNVq2bFjBy+99BLz588HdN/EAZKTk2nQoIEhuxOi2NlaW/CjR1vMHo4ibfYNY+Xf1xWOSgghxLNisERp//799OvXj5kzZxIaGoqZmRnjx4/nyJEjuLq6Eh0dzciRIzlx4oShuhRCEa3rVWHBYCf96/l/XOXA5XsKRiSEEOJZMViiNHXqVEJCQjAyMmLQoEHs37+fadOmUb16dTw9PRk4cCCJiYmMHz+e33//3VDdCqGI/k51eK9HUwC0Wpi66Tz+YXEKRyWEEMLQDDr11r17d3bt2sVXX31FzZr/biKqVquZP38+o0ePJiMjg+nTp7N+/XpDdi1EsZvS3Z4BTnUASMnQ8NbaM4TGJCsclRBClC2JaZlsPhPK7Whl/n01WKK0YcMGPD09ady4cZ7XzJgxgw8++ACtVsvcuXNZvHixoboXothlPwnn3KAqAPcT0xm55rSUDRBCCANJzdDwutcJPvT2Z9zPvorEYLBEqU2bNoW6bsyYMcybNw+1Ws3KlSsN1b0QijA3UbPSoy2NH+4Jdz0qifHrfUnN0CgcmRBClH6f777MlbsPAKhsYaJIDIoUgBk4cCCenp6Ym5sr0b0QBmVtacra0c76sgFnbsby/uYLZGVJ2QAhhCgq77NhbDwdCoC5iRFfDnxekTgUq5TXrVs31qxZo1T3QhhU3aqW/DSqHRYmagD2XrzLF3uuSI0lIYQogsB7CczacVH/+quBLXCoVVGRWBQtKdyqVSsluxfCoFraWeP5RmvURrraYWuP38TzcLDCUQkhROmSmJbJO7+eJTUjC4ChL9RlUFs7xeIpUqK0evVqUlNTDRqIv78/R44cMWibQhS3F5vVZL57C/3rBQeC+PXULQUjEkKI0kOr1TJz20WuRyUB4Fi7EnMGNFc0piIlSt9++y09evRg7dq1PHjw4KkC8PX1ZcKECQwZMoSLFy8WfIMQJdzgdnWZ+XIz/etPdlzi94t3FYxICCFKh9XHbrD7QjgAFc2MWf5GG8wfLmlQSpE2xZ0wYQLr1q3jm2++YdGiRbi6utK3b1/atWtHtWrV8r03IyODgIAAfHx82LNnD3fu3EGr1dKyZUt69OhRpDchREkzoVtjopPSWfn3dbRa+N+m81S2MKGTvY3SoQkhRIl0PPg+8/Zd1b/+drATDWysFIxIp0iJ0nvvvcfw4cNZtGgRe/bs4cCBAxw8eBCA2rVr4+DgQNWqValcuTKmpqY8ePCA+Ph4QkNDuXr1KhkZGYBuiK1evXpMnTqVvn37Gu5dCVECzHy5GdGJ6XifCyNdk8W4n31ZP8aZtvWrKh2aEEKUKGGxyUza6Ifm4dPCk9zseen5WgpHpVOkRAmgZs2afPPNN0ybNo3Nmzfj7e3NvXv3CA8PJzw8XL8Z7qOynwAyNjamW7duDBkyhC5duuR6rRClnUql4pvXWhCfksGfAREkp2sY9dMZNo5vz/O2lZUOTwghSoTUDA1v/3KWmIfFel0dqvNez6YKR/WvIidK2WrWrMnkyZOZPHkyQUFBnDlzBn9/fyIjI4mJiSEtLQ1ra2uqVq2Kvb097dq1o02bNlSoUMEQ8QtRohmrjVg2vDXjfvbl6LX7JKRlMmL1KX6b0IGmNZV51FUIIUoKrVbLx9svcumObr1z/WqWfD/k36eHS4KnTpQe1bRpU5o2bcobb7xhyGaFKNXMTdSsGNGWkT+d5szNWGKTM3hj1Sk2T+hAwxIw/y6EEEpZdfQG287dAcDSVM3KEe2obKlMBe68KFpHSYjywtLUmJ9GvUBLO92UW1RCGsN/PMmt6CSFIxNCCGUcCohg7r4A/etvBzkpVlQyP5IoCVFMKpqb8PNbzjR7+A/B3fhUhq08qdiO2EIIoZTAewlM2ehH9uYFU7s3oW/L2soGlYcymSjduHGD6dOn4+bmRsuWLenVqxeLFy8mOfnJ/yD99ddfjB07lvbt29O8eXM6derE5MmTuXDhQp73HD9+nNGjR9OhQwdat27Na6+9xpYtW2Q7C4G1pSm/jHWhaU3dGr3w+FSG/XiS0BhJloQQ5UN0Yhpj1p0hKV23eXjfFrWZ2r2JwlHl7YkSpYSEBPz9/QkNDc3zmtDQUHbs2PHUgRWVv78/7u7u7N69GxsbG1xdXUlOTsbLy4uhQ4eSmJhY6LYWLVrEhAkTOHbsGLa2tri6ulKpUiUOHDjAsGHD2L59+2P3bNy4kdGjR3PmzBkcHR1xcXEhJCSETz75hI8//tiQb1WUUjYVzNgwrj1NauiSpTtxKQxdKcmSEKLsS8vUPeEWFpsCQAvbyiwY7IRRCVq8/V+FXszt6emJl5cXmZmZgG6fti+++IImTXJmgX5+fsycOZOBAwfm2db9+/eZN28eFy9exMzMjEaNGuHo6Mhzzz2Ho6MjNjZFK8qXmZnJtGnTSE5O5uuvv2bQoEEApKam8t577+Hj48OiRYv47LPPCmzL19eXFStWYGFhwYoVK3BxcdGf27RpE7Nnz+azzz7DxcWFOnXqALqRrC+//JIKFSqwfv16HB0dAQgPD2fkyJFs27aNbt268dJLLxXp/YmyIztZGv7jSa5FJuqTpQ3jXKhfTRZ4CyHKHq1Wy0feFzlzMxaAGhXN+NGjHRamylbeLkihRpR2797N0qVLsbW1ZdSoUbz88stcunSJwYMHc/jw4SfudNasWezdu5fq1atjY2PDuXPnWLx4MRMmTKBLly507tyZ8ePHP3G7e/fuJTQ0lA4dOuiTJABzc3Pmzp2LpaUlmzdvJj4+vsC2tm7dCsDYsWNzJEkAQ4cOpVu3bqSnp7N//3798VWrVqHRaBgzZow+SQKoU6eOPjlbtWrVE78vUTZVr6hLluwfGVl6fcUJgiMLP+ophBClxaKDQWz30z3hZmZsxI8e7ahV2VzhqApWqETpl19+oWnTpuzatYsZM2awaNEitm/fjq2tLZMnT2bfvn1P1OmZM2cYPnw4v/76K2vWrOHo0aP8888/rFy5kvfee4+2bdty69aTbyTq4+MDQM+ePR87V6VKFVxcXMjIyODo0aMFtmVubk7Tpk1p3759rucbNWoEQEREhP5YdtLYq1evx67v2LEjFStW5OLFiznuEeWbLln6d81SxIM0hqw4QcDdp9tDUQghSpJNp2+z1CcYAJUKvh/aGqe61gpHVTiFSpSCgoJwd3fH1NRUf8ze3p7ffvuNVq1aMX369Cdal2RpaUmzZs1yHKtWrRpdunRh/PjxfP/99zlGagorKCgIAAcHh1zP29vbA3D16tVczz9qzpw57N69m3bt2uV6Pnsxd61auhLr9+/fJzo6GhMTE30S9Si1Wq0/HhgYWGD/ovyoUdGcTeM70LxOJQCik9IZuvIk/mFxCkcmhBBP70hQFLN2XNK//qyfY4nZnqQwCpUoGRkZYWX1+LqJChUqsHr1atq3b8/HH3/Mb7/9VqhOXV1duXTpUsEXPqHIyEhAVy08NzVq1MhxXVH5+Phw7tw5TExM9KNX2W3a2NhgZJT7x2qo/kXZU9XKlA3j2tO6nu4bVnxKBm/8eIrTN2IUjkwIIYrucng87/5yVr+H25jODRndqaHCUT2ZQiVKdnZ2XL58OddzZmZmeHl54erqypw5c9iyZUuB7U2ePJljx47h6+v7ZNEWIPvxf3Pz3Oc8s48XpUxAtsDAQGbOnAno1i/Z2toWqm/QfVZP278ouypbmLB+jAvODXWb5mZvd3IoQKZqhRClz+3oZEat+bcMwMvP12JWn+cUjurJFSpRat++PQcOHCA9PT3X8yYmJixdupSXXnqJM2fOFNhenz59ABg1ahSff/45J06cICnp6SsUq9W6lfMFbbJb1HpG/v7+jBw5kri4ONzc3JgyZYr+XPYoUmE2+JV6SiIvFcyMWTfamW5NqwOQlpnF+PVn8T4bpnBkQghReJEJqby5+hRRCWkAtKlnzeIhrUp0GYC8FKo8wCuvvEJUVBRXrlyhVatWuV6jVqtZtGgRNWrU4MqVK/m217NnT65evUpUVBQbN25k06ZNqFQq6tatm6NMQOfOnZ/ozVhZWREXF0dKSkqu51NTUwGwsLB4onYB/vjjDz766CNSUlLo0aMHixcvzjHFlj01md1HbtLSdL8wlpaWT9y/KD8sTNX86NGO6VsusOtCOJosLe9vuUBcSgZjOpeuIWshRPkTn5LByJ/OcPthbbgmNSrw06gXMDcp2WUA8lKoRMnR0ZFFixble423tzfNmjVj+vTpmJjkv6Hd/PnzAV3do+DgYK5evcrVq1cJCAjg+PHj7Nu3D5VKRUBAQL7t/FeNGjWIi4sjKiqKunXrPnY+e21Q9lqhwvL09GTp0qVotVqGDx/OJ598oh+9ypa9Lur+/ftotdpcR5aK2r8of0yNjfhuSCuqWJqw7oTuCdAv91whKiGND3s7lMpvZUKIsi81Q8O4db76J3dtrS34eYwz1pamBdxZchW64GRBZs2ahUqlYt68efkWm8zRubExzZo1e+wJuHv37hXqybT/cnBwICgoiODgYNq0afPY+eDgYP11hZGVlcXHH3/M9u3bUavVfPTRR3h4eOR6rbW1NTVr1iQiIoJbt27RoEGDHOc1Gg3Xr19/ov5F+WZkpGLOgOZUsTLluz+vAeB1JIS78Sn836CWmBmXzm9nQoiyKUOTxaQN5zh9U/cQSlUrU9aPcaZ25SefxSlJntleb/fv3+fevXv6St5PolatWri6uj7xfd26dQPItbRAbGwsp06dwsTEhE6dOhWqvU8++YTt27djaWnJDz/8kGeS9N/+Dxw48Ni5f/75h4SEBJo1a6YvKSBEQVQqFf/r0ZQvBz5P9iDSzvPhjPzpNPEpGcoGJ4QQD2mytLz323n+DNDNnFiZqlk32plG1SsoHNnTM3iitGnTJjp06ECXLl1wc3PDyckJd3d3vv/+e8LDww3dXQ49e/akTp06HDt2jF9//VV/PDU1lVmzZpGcnMygQYNybJGSkZFBSEgIISEhZGT8+4dnx44deHt7Y2xszPLly/VJUH7eeOMN1Go1K1as4Pz58/rj4eHhfPnllwBMmDDBEG9VlDMj2tdnxYh2mJvo/pM9eT2GwV7HuROX+3o8IYQoLllZWj7YeoE9/ncB3dKBHz3a0cKussKRGYZKa6BHsJo1a6Zfl5NbkyqVCrVazYgRI3jvvfdyFK80pFOnTjF+/HhSU1Np3rw5dnZ2+Pn5ERkZiaOjI+vXr6dChX8z3LCwMLp37w7AoUOHsLOzQ6PR0L17d+7evUvNmjVxdnbOs7/OnTvnmGpcuXIlCxcuRK1W4+zsjLm5OadOnSI5OZnBgwfz1VdfGey9uru7c/nyZZo3b862bdsM1q4oufxuxzJmnS8xSbonUGtUNGPVyHa0tCsdFW6FEGWLVqtl1o5LbDh1GwATtYqVI9rh1qzkr8Ut7N9Qg61RyqbVaunTpw9ubm5YW1sTHR3NmTNn8PHxITY2lrVr13Lx4kVWrFiRaxHLp+Xi4sKWLVtYtmwZp0+fJjg4GDs7OwYNGsSYMWNyJEl5CQwM5O5dXWYcERHB7t2787y2UqVKORKl8ePH07hxY9auXYu/vz8qlYrGjRszbNgwXn311ad/g6Jca12vCtve6cioNae5GZ1MZEIar684waLXW9GnRW2lwxNClCNarZYv9wTokyS1kYqlw9qUiiTpSRh8RGnmzJm5ruXJyspi48aNLFiwgNTUVHr27MmSJUsM0XW5JSNK5VdMUjoT1vvqd+EGeL9nUya9aF+oWl5CCPE0tFotX+8NYNWxG4Bu/7bvhrTilVa2CkdWeIX9G2rQNUpqtZqhQ4fm3pGREW+88QZbt27F2tqagwcPcuLECUN2L0S5UdXKlF/GuvBaGzv9sYUHg3jvt/OkZmgUjEwIUdZptVq+2HNFnyQBfOPeslQlSU/CYImSubk5VlZWBa49aty4MTNmzECr1bJ161ZDdS9EuWNmrGbB4JbMeOnf8ho7zofz+ooThMsibyHEM6DVapmz6zJr/rkJ6EaS5ru34PUXHq9dWFYYLFGqWrUqCQkJxMQUvIlnnz59MDY25ty5c4bqXohySaVS8Y5rY7zebIvFw6q3/mHxDFh2TDbUFUIYVFaWlk93XtIXwVWp4JvXWjLUuZ7CkT1bBkuUWrRogVarZcOGDQVea2pqiqWlJdHR0YbqXohy7aXna7Ht3Y7Uraor7HY/MZ3hP55k/YmbsregEOKpabK0zNx2kV9O6hZuq1SwYJATr7cruyNJ2QyWKL366qtotVq8vLwKXFh89+5dHjx4UKQ914QQuXuudiV2TexMZ3tdnbDMLC2f7rzM+1sukJIu65aEEEWTlqlh8sZz/OYbCoCRCha/3orX2toVcGfZYLBEydXVFTc3NzIzM5k1axZTpkzBz8/vsesSExOZNWsWIFt5CGFoVaxMWTv6BcZ1+Xfz3G3n7vDq8n+4HpWoYGRCiNIoOT2Tset8+f3iPUBXJ2nJsNYMbF02F27nxqB1lL777jumTZvGoUOHOHjwIAcPHsTGxoaWLVtSpUoV4uLiOHXqFImJiahUKoYMGWLI7oUQgLHaiFl9HWlhZ81H3v4kp2u4ei+BAcv+4f8GtZR6S0KIQolPyeCttWc4e0tXhsTcxAivN9vi6lC26iQVxKCJkpmZGZ6enuzYsQMvLy9u3rxJVFQUhw4deqxq95tvvknfvn0N2b0Q4hEDnOrgWLsib/9yjuDIRBLTMnn313OM6tiAmX2ayaa6Qog83YtPZdSa01y9lwBARTNjfhr9Ai80qKpwZMXP4JW5AQYOHMjAgQPx8/PjxIkTBAUFERERgbGxMQ0bNmTAgAG0a9fuWXQthHiEfY2K7JzYiY+3X2Tned1ei2uP3+TMzRiWDmtdJjasFEIY1rWIBEb+dJrw+FRAV7ft57eced62bOzd9qSeSaKUrXXr1rRu3fpZdiGEKICVmTHfDWlFuwZV+XLPFdIzs7gc/oB+S4/x1cDncW9TPhZkCiEKdvpGDGPXneFBaiYAdlUsWPeWM43L8Zcqg1bmFkKUTCqVihHt67Pj3U40qq7bYzE5XcO0zRd477fzPEjNUDhCIYTSfr94lzdXn9InSc/bVmLbux3LdZIEkigJUa441qnEnsmdeb3dv6NI2/3u8PJ3Rzl1XeqaCVEeabVafvgrhHd/PUd6ZhYAXZtWZ9P4DtSoaK5wdMqTREmIcsbS1Jj/G+TE90NbUdFMN/t+Jy6FoT+eZN6+ANIypeaSEOVFWqaG6Vv8+eaPq/pjr7WxY/XIdlQwe6arc0oNSZSEKKdeaWXLvv91wbmh7ikWrRZWHLnOQM/jXAl/oHB0QohnLSYpnRGrTuN9Lkx/7P2eTVkwuCUmakkPssknIUQ5ZlfFko3j2jPz5WaYqHUlPALuPmDAsmN892cQGZoshSMUQjwLgfcSGOj5D6dv6vaENDM2wnN4GyZ3b6Iv5yN0JFESopxTG6mY0K0xOyd2plmtioBu+5Pv/rzGK8v+kdElIcqYvf53eXX5P9yOSQagekUzNk/oQN+WUow2N5IoCSEA3ULvnZM6MflFe9RGum+UVx6OLi08EEhqhqxdEqI002RpmbcvgIkbzpH8cP/H5nUqsXNiJ5zqWiscXckliZIQQs/MWM37vRzY8W4nHGr+O7q01CeYPt8f5aQ8GSdEqRSblM6oNadZceS6/ph7a1u83+lIHWvZoD4/kigJIR7Twq4yuyZ3YsqL9hg/HF26fj+JoStPMmOrP3HJ6QpHKIQorLO3Yum75ChHr90HdNPts/s7svB1J8xNZCujgkiiJITIlZmxmmm9HNg7pQtt6v07LP+bbygvLjzCZt9QsrK0CkYohMiPVqvlx7+vM2TFCf12JNWsTPl1rAujOzWURduFJImSECJfDrUqsvXtjnz5SnN9XZWYpHQ+3OrP4BUnuBwer3CEQoj/iktOZ9zPvnz9ewCZD7/QODeoyt4pXWjfqJrC0ZUukigJIQpkZKRiRIcG/DmtW44nY87eiqX/0mPM2XVZpuOEKCGOh9zn5e+P8mdApP7YRLfGbBjnQq3KUmn7SUmiJIQotFqVzfEc3ob1Y5xpZKPbMy5LC2uP38R1wV/8fOImmVJ7SQhFpGdmMW9fAG+sOsXdh1NtVa1MWTv6BT7o3QxjKSJZJPKpCSGeWJcm1dn3vy580NsBi4eLQeOSM/hs52X6LDnK0WtRCkcoRPkSHJnAq8v/YcWR62gfLh3s2Lgav0/pgqtDDWWDK+UkURJCFImZsZqJbvb4TO/GwFZ19MeDIhIZsfo0I386TcBdKVYpxLOkydKy6uh1+i45xuWHxWFN1Co+7tOMX8bIVJshyI53QoinUruyBd8NbY1HxwZ8vvsKF0LjADgSFMXfjPimoAAAIABJREFU16Jwb23H+72aSq0WIQwsJCqRD7f6c/ZWrP6YfY0KfD+0Fc3rVFYwsrJFEiUhhEG0qVeF7e90ZNeFcL7dH8iduBS0WvA+F8Zu/3A82tfnHdfGVKtgpnSoQpRqmiwtPx27wYIDgaRl6tYEqlQwqmMDPuzdDAtTqY1kSJIoCSEMxshIxcDWtrz0fC1+OXmLpT7BxKdkkJ6ZxapjN9h4+jZvdW7I2C6NqGxhonS4QpQ6l+7E8/H2i/iH/VuWo0E1S/5vkBPODasqGFnZJYmSEMLgzE3UjO3SiMFt67L8r2DWHr9JWmYWSekalvoE8/OJW4zr0hCPjg2oZC4JkxAFSUrLZNHBINb8c4PsOq8qFYzu2FD3UIWMIj0zkigJIZ6ZypYmzOzzHG91bshSn2v8diaUDI2W+JQMFhwIYuXf13mrc0NGd2xIZUtJmIT4L61Wy/7LEXyx+7K+ujZA05oVmPtqC9o1kFGkZ00SJSHEM1ezkjlfDWzBhK6N+f7QNbadCyNLCw9SM/nuz2usPnoDj471Gd2pITayhkkIAK5FJPD57iscC76vP2ZmbMSU7k0Y16URpsby4HpxkERJCFFs6la1ZMFgJya52eN5OJhtfnfQZGlJSMvE83AIq47e4PV2dRnftRF1q1oqHa4QiniQmsF3B6+x7sRNNI/sp9iliQ1fDXye+tWslAuuHJJESQhR7BrYWPHtYCcmv9iEH44Es8U3jMwsLWmZWaw/eYsNp2/Tt0VtxnZpSEs764IbFKIMSM/MYsOpWyzxCSYm6d8tgeyqWPBJ3+fo3byWbGSrAEmUhBCKqVfNknnuLZn8YhNWHb3BpjO3SU7XoMnSsutCOLsuhOPcoCpvdW5IT8eaqI3kj4Qoe7RaLb9fvMf/7b/Krehk/XEzYyPedbVnQrdGmJvIYm2lSKIkhFBcHWsLPuvvyJTu9vx84hZrj9/Uf6M+fTOG0zdjqFfVEo8O9Rnctq4s/BZlglar5Z/gaBYcCOT8w0Kt2fr/f3v3HhdVmfAB/DfAcBNkQOSOayaDiIKpZa6WCmLrNTXfXbeL2YbaWlmavelatPEJ17Xy3UVNbd98W29l5CUxXdTA0iwyQPAKAir3Owg4DMzAef+gGR3hyAgHGIbf9/Ph42fOc54zz3mcOec35zznnGAvvPU7f/g48xR0d2NQIiKTobC31g9UPZCSj+0/XENmSS0AIKdChfe/uYwPj6XjyWBvPDf2NxjmzbsPU8+UmF2Oj45n4OdrFQbTHx3kgr9MC+ApZxPCoEREJsfO2hJPjxmA+Q/74vurpfj09DWcutp85Y9a04S9v+Ri7y+5GOGrwNOPDMCMYE/YW3NzRqbv52sViP72qsGVbADg7+6IVVOHYKJ/f45DMjHcshCRybKwkGGivxsm+rshs6QWu366gX1Jeaip1wIAzuVW4VxuFSIPX8KsEV6Y/7Avhns7cUdDJkUQBJxML8XmhEz8csdz2QBgUP8+eH2yEjOGe8KCY/BMEoMSEfUIg90c8NdZgXjzCX8cSMnHrp9u4EpRDQCgtl6LPYk52JOYA6W7A+aN8sHsEd5w68snp1P30TQ24cj5Qmz9LhuXC6sNyga42OO1UD88OcILVpa8H5IpY1Aioh6lj40Vnn30N3hmzACk5t3EFz/n4FBqAVQNjQCAjOJarD1yBeuOXsEEZX/MfsgbYUPdeWqOukyVqgF7fs7BjjM3UFStNijzc3PA0kkPYmYQA1JPwS0HEfVIMpkMI3wVGOGrwNszhuJwagG+SsrTn9poEoCE9FIkpJfCTm6JKYHumBXshcf8+vOOxtQpLhVUY1fiDexPzoNa02RQFuzjhKWTBiMswJ2n2HoYBiUi6vEcbKww/5EBmP/IAFwru4X9yXnYn5yP/Ko6AECdphFfnyvA1+cK0NfWCmFDPTBtuAfG+7nCxor3p6H2U2sa8U1aIXYl3kBKjuEl/jIZMDnAHS+OfwBjHnDh2LkeikGJiMzKA6598MYUfyyfrMTZ6xX4OrUAR84XokqlAdD8fLl9yXnYl5wHRxsrhAa4YUqgBx5X9oeDDTeJ1DZBEHA+/ya+SsrD1+cKcLNOY1Bub22J34/2xcLfDsRAVz5upKfjVoGIzJKFhQxjBvXDmEH98NeZgTh1tRSxqQU4cbkEtb9eNVdTr8XBcwU4eK4A1pYWGDe4HyYPdcckfzd4Key6eQ3I1BRXqxGbWoCYX/KQXlzTonyIhyOeefQ3mD3CC462vCmquWBQIiKzZ21lgdAAd4QGuEOtacTpq2U4cqEQxy8Vo0bdHJoaGpv0Y5qA5p3epCFumOTvhocGKCDnwNteqeJWA45eKERsagESr1VAEAzLbeUWmDbME888OgAjBzjz9JoZMsugdO3aNWzevBlJSUkoLy+Hh4cHpk6diiVLlsDevv23g6+srMTMmTMRGBiIbdu2ic536NAh7NmzB+np6dBqtfD29sYTTzyBRYsWwcHBod3vT0QdZyu3xOSh7pg81B0N2iYkXivH8UvFOHax2OAKpStFNbhSVIMtJ7PgYGOFRwf1w+NKV4wf7IoHXPtwh2jGSqrViLtUjGMXi/BjVjm0TUKLeUb/xhnzRvlgepAnjx6ZObMLSmlpaXj++eehUqkQFBSE4cOHIzk5GVu3bkVCQgL27NnTrrCiUqnw6quvorS09J7zvf/++9i5cyesrKwwevRo2NnZISUlBVu3bsWJEyewa9cuODs7t3f1iEhC1lYWeMyvPx7z64/3ZgXifP5NJFwpRXx6CdLyqvRHD2rrtThxuRgnLhcDADydbDF2UD88Oqgfxj7YD74ufB5XTyYIAq4U1eBkeimOXSpqMShbZ5BrH8wM9sKTI7wwqD9/9PYWZhWUtFotVqxYAZVKhaioKMybNw8AoFarsXz5csTHx2PDhg2IiIi4r+Xm5uZi+fLlOH/+/D3nS0lJwc6dO6FQKLBr1y74+fkBAGpqavDSSy/hl19+wcaNG+/7/Ymo88lkMgT5KBDko8Brk/1QVluP79JL8f3VUpy+WobyXx/SCwCFN9XYn5KP/Sn5AAAvJ1s8/IALRg90wcMDnaF0c+Ql4CbupkqDH7PL8V1GCRKulLa435GOt8IO04M8MSvYC4FefXkksRcyq6D0zTffIDc3F2PHjtWHJACwtbXF2rVrERISgi+//BKvvfYanJzafpimWq3Gjh07sG3bNtTW1sLX1xe5ubmi83///fcAgJkzZ+pDEgA4Ojpi6dKl+NOf/oTExMQOrCERdRVXBxs8NcoHT43yQVOTgMtF1Th1tQynr5bhlxsVBvfJKbip1t9+AAAcba3093h6aIACI3yd4dLHurtWhdB8VDD5RiV+yCrDj1nluJB/E62cUQPQ/Ny1JwLdMSXQg+GIzCsoxcfHAwDCwsJalDk7O2PMmDFISEjAqVOnMGPGjDaXd+TIEXz00UdQKBSIioqChYUFVq9eLTq/pWXz/ViKiopalOlO2fG0G1HPY2EhQ6CXEwK9nPDShAfRoG1Cal4Vfswqx0/Z5UjJqUKdplE/f41ai1NXy/QP8gWaj0wM93bCcB8nBHr1RaCXE/o72nTH6pg9QRBQcFON5BuVSLpRibPXK3C5sFo0GFlbWWDsoH6Y5N8fE/3deEk/GTCroJSRkQEA8Pf3b7V88ODBSEhIwJUrV4wKSgqFAkuXLsULL7yAvn37Yv/+/fec//HHH8fGjRtx/PhxbNy4EX/4wx9gb2+PM2fOYN26dbC0tER4ePj9rxgRmRRrKws8PNAFDw90wbJQP2gam3CpoBpnr1fg7PUKJOdUobSm3qBOflUd8qvq8J+Lt39IuTpYI8CzL4Z4OMLfoy/83Bww2M0BfXg/J6MJgoCiajUuF1bjfF41UvOqkJZXhbLahnvWG+LhiN8+6Irxfv0wdpAr7Kx541FqnVl9G0tKSgAA7u7urZa7ubkZzNeWkJAQhISEGP3+QUFBiIiIwAcffIBNmzZh06ZN+jJfX19ER0fjkUceMXp5RNQzyC0tEOyrQLCvAuGPDdIf0UjJqcS5nCqk5lXhYkG1/nl0OmW1DS2OPAHNR58GuzngAdc+Bn+eTra99vlggiCg/FYDMktqkVVai6vFtbhSVI0rRTX6m4mKkcmaT6eNHuiMR38dhO/qwKN5ZByzCkoqlQpA85ik1uim6+brDI888gjGjRuH06dPY/jw4bC1tcWFCxeQm5uLbdu2wc/Pj6ffiMycTCaDt8IO3go7zAjyAgA0Ngm4VlaL8/k3cSG/GleKqnG5sAYVt1oe+dAdffouw/AqWysLGbwUdvB1sYOvsz28FXbwVNjB08n21z+7Hn1kRK1pROFNNQqr6pBXVYecchVuVKiQU34L18tVLe6ALcbJTo4gHycE+ygwaqAzRg5whpMdL+Gn9jGroGRpaYmmpqY2B94Jd98xTCKnT5/Gyy+/jAEDBuDw4cPw9fUFANy6dQsRERE4fPgwXnzxRXz11VewsOidvwqJeitLCxkGuzlisJsj5jzUPE0QBJTW1ONSYTUyS5qPkmSU1CCzuBY1v949/E7aJgE5FSrkVKgAlLf6Po42VujvaIP+jjZwdbRBvz7WcLa3hksfayjs5XCyk6OvnRx9beXoa2uFPjZWsJNbSn6VXmOTgFsNWtyq16JWrUVVnQZVKg2qVA2oUmlQdqsepTX1KKttQFlNPYqq1a2Gxra4OdpgiGdfBHg6YqhnX4zwVWCAiz0HYJNkzCoo9enTB1VVVairq2u1XK1uvvzTzk76RxM0Njbi3XffhVqtxvr16/UhSdeutWvXIi0tDRcvXkRCQgJCQ0MlbwMR9SwymQxufW3h1tcWE/3d9NN1Aepa2a3mv/JbuF52C7kVdcitULUaonRq6rWoqdciu+zWfbXFVm4Be+vm0CS3lEFuaQFrKwtYWVrAUtbcVotf/21qEtAoCPp/NVoBDY1NqNc0ol7bhDpNY4vTjB0hkwGefW0xqH/zGK4H3RzwYP8+ULo78hQadTqzCkpubm6oqqpCaWmpQVDR0Y1N0o1VklJOTg7y8vLg6uqKgICAFuU2NjYYO3YscnJycOHCBQYlIhJ1Z4AaM6ifQZkgCLhZp0FuRR0KbtahsKoOhTfVKLipRnG1GmU19Sipqdc/z85Yak0T1Jr7P6IjBSsLGdwcbeCpsIOXwg5eTrbwUthhgIs9BvRrPsVoK++5pxSpZzOroOTv74+MjAxkZmZi5MiRLcozMzP180nt5s2bAG7fIqA1ujKt9v42YEREOjKZDAp7ayjsrTHcR/x+cKoGLcprG1BxqwEVqgZU1DagUtWAarUW1XUa1Ki1qFZroGrQQtXQiLqG5qNAak0jNI1NaNA2QdPYfKRIvC2Apaz56JON3AI2VhawsbKErdwCfWys4GBjhT7Wzaf3FPZyONvL4WRvDSc7OVwdrNHfofkUoZOdnKfKyGSZVVCaMGECYmNjERcXh9///vcGZZWVlUhMTIRcLse4ceMkf++BAwfC0tISxcXFuHjxIgIDAw3KtVotfvrpJwBo9YgTEZGU7K2tYO9iJcnjVQRBQJNw+18LWfOYK4Yb6g3MakRxWFgYvLy8cPr0aezevVs/Xa1WY82aNVCpVJg3bx5cXV31ZRqNBllZWcjKyoJGY9wVFa1RKBSYPn06AGDVqlUoLCzUl9XX1yMyMhLZ2dnw9fXF5MmT2/0+RERdTSaTwdJCBqs7xi0xJFFvYVZHlGxtbbFu3TosXrwYkZGR2LdvH3x8fJCSkoKSkhIMHToUK1euNKhTXFyMadOmAQC+/fZb+Pj4tPv9IyIicP36daSlpSEsLAwPP/wwbGxscOHCBZSWlsLV1RWbNm2CtTUfZUBERNQTmFVQAoAxY8YgJiYGmzZtws8//4zMzEz4+Phg3rx5ePHFF+Hg0HlPfHZ0dMTu3buxZ88exMbG4ty5c9BoNPD29sb06dMRHh6O/v37d9r7ExERkbRkQmfdVIg63dy5c/Xjodp6vAoRERHdZuw+1KzGKBERERFJiUGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEWHV3AzrDtWvXsHnzZiQlJaG8vBweHh6YOnUqlixZAnt7+3Yvt7KyEjNnzkRgYCC2bdsmOl9+fj62bduGU6dOobS0FA4ODhg9ejT+/Oc/IzAwsN3vT0RERF3L7I4opaWlYe7cuYiNjYWrqysmTpwIlUqFrVu3Yv78+aitrW3XclUqFV599VWUlpbec76kpCTMmjULe/fuhZ2dHSZNmgRnZ2ccP34c8+fPx7lz59r1/kRERNT1zCooabVarFixAiqVClFRUYiJiUF0dDROnDiBkJAQpKenY8OGDfe93NzcXCxYsABnz56953w1NTV4/fXXUVtbi7feegtHjhzBxo0bceTIESxbtgwNDQ347//+7/auHhEREXUxswpK33zzDXJzczF27FjMmzdPP93W1hZr166Fvb09vvzyS9y8edOo5anVanzyySeYPXs2zp8/D19f33vOv3fvXpSUlGDmzJn405/+pJ8uk8mwdOlS+Pv7QyaTobCwsH0rSERERF3KrIJSfHw8ACAsLKxFmbOzM8aMGQONRoNTp04ZtbwjR47go48+gpWVFaKiorB06dJ7zn/06FEAQHh4eIsymUyGQ4cOIS4uDp6enka9PxEREXUvswpKGRkZAAB/f/9WywcPHgwAuHLlilHLUygUWLp0KY4fP25whKo1Go0G6enpsLe3h7+/P4qLi/F///d/eOedd7B27Vp8991397EmREREZArM6qq3kpISAIC7u3ur5W5ubgbztSUkJAQhISFGzZufnw+NRgMvLy8cPnwYERERUKlU+vJ///vfGDduHKKjo+Hg4GDUMrvNhg3Nf20ZORI4dMhw2qxZQHJy23VXrGj+06mpAQICjGvf118Do0bdfn34MPDSS23Xc3AA7g7Jb74JfP5523WnTwfuvtJx9GigqKjtuuvXA08/fft1ejoQGtp2PQA4exa48wjkJ58AkZFt11MqgV+PsOo98wxgTGBftAh4913DaT4+bdcDgF27gIkTb78+eRJ49lnj6ublGb5+7z3gX/9qu96ECcDu3YbTQkKAX3843VNEBLB48e3XhYXAww+3XQ8Avv0WuPNH2Z49gDFjED08gF9+MZy2ZAnwzTdt1/3jH4EPPjCcNmQIYMxFKlu3AjNm3H6dlAQ8+WTb9QDg8mXA0fH2a24jWuI2ou16gLTbiC5iVkFJF0xsbW1bLddNvzPASKWmpgYAUFpailWrVmHy5Ml45ZVX4OnpidTUVERGRuKHH37Am2++iS1btkj+/pKqrgby89uer7UxW6WlxtWtrjZ8LQjG1QOAhgbD13V1xtW9c0OvU1lpXN2KipbTioqMq3v3502rNX5dGxsNX9fWGlfXyanltLIy4+q2NobP2PbW17d8bWzd1tphTN2yspbTiouNq3t3wGhsNL69Wq3ha5Wq/etaUWFc3crKltMKCppDRFvq6gxfNzQY315BMHzNbURL3Ea0XQ+QdhvRRcwqKFlaWqKpqQkymeye8wl3f+klUP/rf75KpcL48ePxz3/+U182btw4fPrpp5g+fTri4+ORlpaGoKAgydsgmb59AW/vtufr37/1acbU7dvX8LVMZlw9ALC2NnxtZ2dc3daO5Dk7G1fXxaXlNA+PtusBwN337rKyMn5dLS0NXzs4GFe3taOqrq7G1W1tA2pse21sWr42tm5r7TCmrqtry2nu7q1vzO9292fC0tL49lrdtfm0tzeubmufGxcX4+o6O7ec5uVl3BElOzvD19bWxq/r3dtUbiNa4jai7XqAtNuILiITOiM1dJMxY8agqqoKJ06caPUKtR07diAqKgozZ87Ehx9+eN/L379/P1avXo2JEye2uOHkxYsXMXfuXADAJ598ggkTJrSov2zZMsTFxWHFihVYsmTJfb//3ebOnYuLFy8iMDAQ+/fv7/DyiIiIegtj96FmNZhbNwZJ7KaQurFJuvmk5HrHr1ofkXO1uumVrR0+JyIiIpNjVkFJd7VbZmZmq+W66WJXxXWEu7s7FAoFAPHB4mW/jqVwae0QLREREZkcswpKutNdcXFxLcoqKyuRmJgIuVyOcePGdcr7T/x1JP+hu6/yQPPNKxMTEwE0nyIkIiIi02dWQSksLAxeXl44ffo0dt9xubBarcaaNWugUqkwb948g9NkGo0GWVlZyMrKgkaj6dD7v/DCC5DL5Thw4AD27dunn97Q0IDIyEgUFRVh5MiRCA4O7tD7EBERUdcwq6vebG1tsW7dOixevBiRkZHYt28ffHx8kJKSgpKSEgwdOhQrV640qFNcXIxp06YBAL799lvR8UXGGDJkCN577z288847+Mtf/oLPPvsMvr6+uHjxIoqKiuDp6Yn169d3aB2JiIio65jVESWg+bRWTEwMnnjiCRQUFODkyZNwdHTE0qVLsXPnzk6/2eNTTz2FmJgYTJ06FRUVFfj+++8hl8uxcOFC7N+/v83nxREREZHpMKvbA/Q2vD0AERFR+/TK2wMQERERSYlBiYiIiEgEgxIRERGRCLO66q23yfv1ScpZWVn6x6cQERFR27KysgDc3peKYVDqwXQP4lWr1bh48WI3t4aIiKjn0e1LxTAo9WAuLi6oqKiAjY1Nh+7/RERE1Nvk5eWhvr6+zceK8fYARERERCI4mJuIiIhIBIMSERERkQgGJSIiIiIRDEpEREREIhiUiIiIiEQwKBERERGJYFAiIiIiEsGgRERERCSCQYmIiIhIBIMSERERkQgGJSIiIiIRDEpEREREIhiUiIiIiEQwKBERERGJYFAiIiIiEmHV3Q2gznXt2jVs3rwZSUlJKC8vh4eHB6ZOnYolS5bA3t7+vpZVXFyMjz/+GGfOnEFRURFcXV0REhKCl19+GS4uLp20BqZHyj49efIkdu3ahQsXLqCmpgYKhQIjR45EeHg4goODO2kNTIuU/Xm3v//979i+fTteeeUVvPrqqxK12PRJ2acqlQrbt29HXFwccnJyYGFhgYCAACxYsAC/+93vOmkNTIuU/Xnu3Dls27YNycnJuHXrFvr164ff/va3+POf/4wBAwZ00hqYtuvXr2P27NmYO3cuIiIi7qtuV+yXZIIgCJIsiUxOWloann/+eahUKgQFBcHT0xPJyckoLS2Fv78/9uzZAwcHB6OWlZubiz/+8Y8oLS2FUqnEAw88gEuXLiE3NxceHh7Yu3cvPDw8OnmNup+UfbphwwZs27YNMpkMgYGB8PDwQHZ2NrKzs2FpaYmoqCjMmTOnk9eoe0nZn3f74Ycf8OKLL0IQhF4VlKTs07KyMjz//PPIzMyEq6srRowYgfLycpw7dw6CIGD16tVYuHBh565QN5OyP48ePYo33ngDjY2NCAwMhJeXF9LT05GTk4M+ffrgs88+Q1BQUCevkWkpKyvDggULkJWVhWeeeea+glKX7ZcEMksajUYIDQ0VlEqlEBMTo59eV1cnvPTSS4JSqRTee+89o5f39NNPC0qlUvjnP/+pn6bVaoWIiAhBqVQKixcvlrT9pkjKPj179qygVCqF4OBg4aeffjIo+/zzzwWlUikMGzZMyM/Pl3QdTInUn9E7lZeXC+PGjROUSqWgVCqF6OhoqZpt0qTu08WLFwtKpVJ49dVXBbVarZ/+ww8/CIGBgUJAQAA/o0b2p0qlEkaPHi34+/sLsbGx+ularVZYu3atoFQqhRkzZki+Dqbs0qVLQlhYmP57er/f967aLzEomamDBw8KSqVSeP7551uUVVRUCCNGjBACAwOFqqqqNpel26lPmTJFaGxsNChraGgQJk6cKCiVSuHq1atSNd8kSdmnb731lqBUKoWNGze2Wr5o0SJBqVQK27dv72izTZaU/Xm3JUuWCEOHDhXmz5/fq4KSlH2ampoqKJVKYfLkyQYhSeedd94RJk2aJMTFxUnRdJMkZX+eOXNGNAzV1dUJAQEBglKpFMrLy6VoukmrqqoS1q9fLwwbNkxQKpVCSEjIfQelrtwvcTC3mYqPjwcAhIWFtShzdnbGmDFjoNFocOrUKaOXFRoaCgsLw4+MXC5HSEgIAODbb7/taLNNmpR9amtrC6VSiUcffbTV8kGDBgFoPv9urqTszzvt3r0bCQkJePnllzFs2DBJ2tpTSNmnR48eBQA899xzsLGxaVEeGRmJ+Ph4TJkypYOtNl1S9qelpSUAoKKiAg0NDQZllZWVaGxshFwub/ep5p5kx44d+N///V+4uLhgy5YtmD179n0voyv3SwxKZiojIwMA4O/v32r54MGDAQBXrlwxellKpbLDy+rJpOzTv/71r4iNjcXo0aNbLU9NTQUAsx73JWV/6ly9ehV///vfMXLkSCxZsqTjjexhpOzTCxcuAABGjBgBlUqFAwcOIDIyEu+++y6++uorqNVqiVptuqTsz+HDh8PFxQVlZWV44403kJ2dDbVajdTUVLz88ssAgIULF8La2lqi1psuDw8PvPXWW4iLi9MHmvvVlfslXvVmpkpKSgAA7u7urZa7ubkZzNfBJqK/AAAJPklEQVRVy+rJuqof4uPjkZycDLlc3uovWXMhdX/W19djxYoVkMvl+OCDD/S/4HsTKfv0+vXrAJqPdsyYMQP5+fn6si+++AJbtmzB1q1b4efn18FWmy4p+9POzg6bNm3C8uXLcezYMRw7dkxfZmtri8jISPzhD3+QoNWm77/+6786vIyu3C/xiJKZUqlUAJq/gK3RTdfNZ8yy7OzsOrysnkzKPhWTnp6O1atXAwDCw8Ph7e3d7mWZOqn7c/369cjIyMA777wDHx8faRrZw0jZp7W1tQCAlStXwtHREbt27UJSUhK+/vprPPbYY8jLy8OiRYv085kjqT+jDzzwAGbNmgVLS0sEBgYiNDQUvr6+UKvV+Oyzz3D+/HlpGt4LdOV+iUeUzJSlpSWampogk8nuOZ9gxN0hdL/MpVhWTyZln7YmLS0NixcvRlVVFSZNmoRly5a1azk9hZT9qbsf1bRp09o13sFcSNmn9fX1AABra2vs2LEDTk5OAIAhQ4Zg69atmDNnDjIyMvDFF18gPDy84403QVL2Z2FhIZ599llUVlbi008/xdixY/V1//3vf+Nvf/sbXnjhBcTGxsLT01OS9puzrtwv8YiSmerTpw8AoK6urtVy3fgCsTTeWcvqyTqzH/7zn/9gwYIFqKysxOTJkxEdHd1igKK5kao/y8rKsHr1anh6euK9996TtpE9jJSfUd0v8tmzZ+tDko6VlRXmz58PAPjxxx/b3V5TJ2V//s///A/y8vKwbNkyfUgCmnf0CxcuxMyZM1FTU4PPPvus4w3vBbpyv2TeW+JeTHd+trS0tNVy3Xlb3XxdtayerLP6YfPmzXj99ddRV1eHp59+GtHR0b1iQKdU/fnxxx+joqICCoUCkZGRWLlypf7v9OnTAIBjx45h5cqV2LJli4RrYHqk/Iy6uroCgOhpTN30ysrK+25nTyFlf545cwYA8Nhjj7VaPnHiRAC3B9HTvXXlfolByUzprtLIzMxstVw3Xexqjs5aVk8mdT80NTVh1apV+qNHa9aswbvvvttrBiFL1Z+6MQiXL19GbGyswV92djaA5itkYmNj9Tsrc9UZ33uxW1TodlDm/PgiKfvz5s2bAJqPxrVG973XarX33c7eqCv3SwxKZmrChAkAgLi4uBZllZWVSExMhFwux7hx44xe1vHjx9HU1GRQptFo9PepmDRpUkebbdKk7FMAePvtt3HgwAHY29tjy5YtWLBggaTtNXVS9ee6deuQnp7e6p+uT1955RWkp6dj586d0q+ICZHyM6o7wnH06FFoNJoW5d9//z0A4JFHHulAi02blP354IMPArh9/5+76Y5+BgQEtLe5vUpX7pcYlMxUWFgYvLy8cPr0aezevVs/Xa1WY82aNVCpVJg3b57+8DrQ/OHKyspCVlaWwYZx5MiRGD58OLKysrBhwwb94LjGxkZERUWhsLAQjz/+uNl/waXs04MHD2Lfvn2wsrLCxx9/rP/S9yZS9ic1k7JPp02bBh8fH1y/fh2RkZEGZTExMYiLi4OTkxOeeuqprlm5biBlfz7zzDMAgE2bNuHs2bMG7/PVV19h3759kMvlePbZZzt5rXoWU9gv8aG4ZiwxMRGLFy+GWq1GYGAgfHx8kJKSgpKSEgwdOhQ7d+40uAtsXl4eQkNDATTfzfTOsQlXr17Fs88+i6qqKgwaNAh+fn64fPkycnJy4O3tjc8//1z0fhbmRIo+bWxsRGhoKAoLC+Hu7n7PX+Tjx48366u4pPyMtiYqKgo7duzoVQ/FlbJPL1y4gPDwcFRWVsLNzQ3BwcG4ceMGMjIyYGNjg3/84x/tvmFgTyFlf0ZERGDv3r0Amm9A6eHhgczMTFy7dg1yuRxRUVF48sknu3YFTcDGjRuxadOmVh+Kawr7JR5RMmNjxoxBTEwMnnjiCRQUFODkyZNwdHTE0qVLW3y52+Ln54f9+/dj7ty5qKmpQUJCAoDmxxt8+eWXvSIkAdL0aXp6OgoLCwE0j/+4e1zNnX9paWmdvUrdSsrPKDWTsk+HDRuG2NhYPPfcc7C2tsbJkydRWVmJ6dOn48svvzT7kARI25+RkZHYvHkzxo8fj9zcXCQkJKC2thYzZsxATExMrwxJHdFV+yUeUSIiIiISwSNKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiIiISASDEhEREZEIBiUiIiIiEQxKRERERCIYlIiIiIhEMCgRERERiWBQIiIiIhLBoEREREQkgkGJiKiDkpKS4O/vD39/fxw9erTVeVJTU/HQQw/B398f69ev7+IWElF7MSgREXXQqFGjEBISAgCIjo5GY2OjQXl2djaWLFkClUqFOXPm4M033+yOZhJROzAoERFJYOXKlbC0tER2djYOHTqkn15cXIzw8HBUVlZi0qRJeP/99yGTybqxpUR0PxiUiIgk8OCDD2LOnDkAgE2bNkGj0aC6uhrh4eHIz8/HqFGj8I9//ANWVlbd3FIiuh8yQRCE7m4EEZE5KC4uxpQpU6BWq7F69WqcOHECZ8+ehVKpxO7du9G3b9/ubiIR3ScGJSIiCX344Yf417/+pX/t7e2Nzz//HO7u7t3YKiJqLwYlIiIJlZSUYMKECWhqaoJCocDevXsxcODA7m4WEbUTxygREUlEq9UiIiICTU1NAIC6ujrY2tp2c6uIqCMYlIiIJCAIAt5++20kJCTAxcUFPj4+qK+vR3R0dHc3jYg6gEGJiEgC69evx4EDB2Bvb49t27Zh+fLlAICDBw8iMzOzm1tHRO3FoERE1EGffvoptm/fDrlcjo0bNyIoKAjTp0+Hv78/Ghsb8dFHH3V3E4monRiUiIg64ODBg/jggw8gk8nwt7/9DePHjwcAyGQyvPbaawCA+Ph4JCUldWcziaidGJSIiNrpu+++w5o1ayAIAlatWoWZM2calIeGhiI4OBhA820DiKjnYVAiImqHlJQUvPbaa9BqtVi0aBEWLlzY6ny6sUrJyck4ceJEF7aQiKTA+ygRERERieARJSIiIiIRDEpEREREIhiUiIiIiEQwKBERERGJYFAiIiIiEsGgRERERCSCQYmIiIhIBIMSERERkQgGJSIiIiIRDEpEREREIhiUiIiIiEQwKBERERGJYFAiIiIiEvH/uFl5TJBcLa0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now the variance on the same test points\n",
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.plot(x_star, v_star, lw=2, label='$\\sigma_n^2(x) + \\sigma^2$')\n",
    "ax.plot(x_star, gpm.likelihood.variance * np.ones(x_star.shape[0]), 'r--', lw=2, label='$\\sigma^2$')\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$\\sigma_n^2(x)$')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the variance is small wherever we have an observation.\n",
    "It is not, however, exactly, $\\sigma^2$.\n",
    "It will become exactly $\\sigma^2$ in the limit of many observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having the posterior mean and variance, we can derive 95\\% predictive intervals for $f(x^*)$ and $y^*$.\n",
    "For $f(x^*)$ these are:\n",
    "$$\n",
    "m_n(\\mathbf{x}^*)) - 2\\sigma_n(\\mathbf{x}^*) \\le f(\\mathbf{x}^*) \\le m_n(\\mathbf{x}^*)) + 2\\sigma_n(\\mathbf{x}^*).\n",
    "$$\n",
    "Let's plot this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "f_lower = m_star - 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "f_upper = m_star + 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "ax.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5)\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, on the same plot, let's superimpose our predictive error bar about $y^*$.\n",
    "This is:\n",
    "$$\n",
    "m_n(\\mathbf{x}^*)) - 2\\sqrt{\\sigma_n^2(\\mathbf{x}^*)+\\sigma^2}\\le f(\\mathbf{x}^*) \\le m_n(\\mathbf{x}^*)) + 2\\sqrt{\\sigma_n(\\mathbf{x}^*) + \\sigma^2}.\n",
    "$$\n",
    "Let's use red color for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1a30a190>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vxe0HD+LKK66QAXBeH2ZVAJxdw+x8ATPzRdTrw7escLG4rEZYhBCYqwGnyw5OlQXOVARqDgCU8dDLZVy6I42dE+t59d2htBBCRo9yuS0qKpU2m5WVFu776VvuOHhwVduaD998M6648kr8pyuuwHxDw2xVIDNisfrXXHvTORWWkBk5R1iEEMjVgVOupJwuC1SWiJyJ+HREjN78bFBaCCGjQbm88OinczFhOExRGRDOKyxeb6up1tY8mAqP4Ud5gVypjJm5Yt8EwG0Ujx97cIGwALLi8vixB/GWt92IU2UhRcUWKC1TbArqwJaghjeNB3DwjWmkQ71ZN0FpIYQML5VKW1RURSWXk6JimjJLhYsJBx9Nk6PKkQgahoH5qsCMJZCr1DGbKWJ2vgi7XOv1VW44i5tug2YEZVdgHn3oi/j+vIPYr97Q9b/168BUQMNUUMPWoI6UX6YP7x4PIB3s3c8Lf1IJIcPFcqISCklR2baNojIMqKbaUAgFR8dsVWDebiKTL7eaagdlVHmtWSwsW685CM8v34Dcv/09cv98HwC07mO/egM8GrClJSkaxg0Neh+O8POnlhAy+ChRmZ1tLyTM52WmihKVrVu5QXkY8HjaW5V1rxxVLgrk7Spm5mVVpVYfzFHltSBXF3j00Qfxw//5pdbH4lcdhP7LN0AArcpKp7hcGtXw7utugrcPJWUxlBZCyGDSraKyWFSmpgZaVJ48fnzFTacX8viBIhQCwmE0A0Fk68Bs2UGmJptqZ0ekqbYbVUc2zb5sC7xiO3jlyXYlBZDCokQl4QO2BnVse89NeCGh49i3ZCXmyW9/CTGfNhB5LZQWQsjgoJppO6d+OkUlFht4UVHccd99Kx7vBdpR97cfOIA7Dh5c/wvcCPx+WVUxTZSEPP6Zy8v9P7NzBcxnS2j2YZz+eiLcvJSXXVF5tSKg/g9UTj+zQFjSv34Qb7rmvdgW1LE1qCHqa1dSpn/zJnj0hTkuO6ff0PdR/pQWQkh/Y9ttUVGSsrhHZUhERfHk8eO48+hRAGhF2C8nLp27ee48enRVY8F9h663jn9qXh/mqu2k2rn5Imbmi6hU672+yg3Fbgi8UhZ4yXbwii1QXmL4KTT1Bmy96n049c9fw1XvvhnvfteN0JY58unMcXnHde/ve2EBKC2EkH7EsoC5OXn0Uyh0F5Uh7lG5ct8+3HXoUEtElhOXxcsE7zp0aDCFxT3+cYLu8U9VIFtoYj5nYWa+gHyh3Osr3DAcIfBaVVZSXrJlZWUp4j5ge0jH9qCGLUEN/ukDOPnmy1csINdce9NAVFgUlBZCSH9QKrUrKotFJRweuakfJSjLiUs3YVnJUVLf0HH8Y7mLCudz7vHP/Ghlqlgd1ZSXbYHqEt+2XwO2hjRsD2rYHtIXHPkoVisggyIsAKWFENJLCgVZUVGiovpUVDJtIjHSOSrLicvACovH01pU2Hn8ky/XMJspYXa+iHJl+DNVhBA4W5WVlBfPU01J+4EdIR3bQxo2BTR4BmDKZ70YzWcCQkhvEEJKiRKVYrFdUSmXGaHfhW7i8hdf/zoyhULrMX0vLJoGBIOt6Z/couOf2fkicoXhWFS4HNWmbKB9yXLw0jK9KX4drUrK9pCGsHd0JWUxlBZCyPriOFJK5ubkrVhsLyWsVuUywrExKSwUla4sFpeBERY3/A2miaIjd//M5x3kRuT4RwiBbB140XLwoi3w845Jn8WoasoOt5rSj8Fu/QClhRCy9jSbMuRtdhaYn19YUanX5Wjy5KQUFV3v9dUOBIf37z+nwpKMRvtPWLze1vFPVfdiriY3Kucrdcy64W/DPP3TFDI35SVb4EXLQX6JnDufBmwLaa1jnwirKSuC0kIIWRsaDSkos7NAJtOuqOTzstoSiwGbN0tR4W+Rq+bIAw8sEBZAVlyOPPBA78VF01qi0jQMZGoCs2WBrBv+NjdfRL44vNM/dlPgJUvgRbeJtr5EOSXmA3a61ZQtQW0gEmj7DUoLIeTCqVbbxz7ZbFtUCgX5QhaLyYkf06SoXASLm26T0WhLYFaS47JuuH0qIhhEvqlhzt39kyvI45/5XAnOEIa/CSGQqQMn3WOfVyvdv0cdwOaAhp2mhp0hHQk/fwYuFkoLIWR12Ha7kTaXax/9FAoyNyUWA3btki9o5KJZakqo8+MbKi6LxpTnagJzebn7Z3a+iLlMaSh3/zSF7Ek5aS1/7BPQgR0hDTtNmZ1ieCgqawmlhRCyPEK0R5NVI63KUSkU2vH5k5Oy8ZKsGcuNNa8kx2XNUEsKTbM1pjxXEshV6pjPlDCbKcKyq2v/dXtM1ZEBbyfdaZ+lslOSPmCnqWMnm2jXHUoLIeRcHEce98zNLWykLRRkpcU0h2rPTz+ykhyWdRUXXW+l1Db8BrJ1gbmK7FPJ5GzMZorIF2yIITv9KTakpJy0ZENtN0/RAGwJatjlVlTiXQLeyPpAaSGESOp1KSid/Slq10+9LkeTUylmqGwATx4/vuLguG7icsWll154lH8oBJgmnGAQhYaGuZpAxnaQLZQxmykik7OGakxZCIH5GnDSdvCCtXTIm9899tnlTvsEeOzTEygthIwyqj9lfl6KSqnUrqgAspqyZYusrHA0ecO4ct8+3H7gwIq3PHeKy+0HDqxeWFSeSiiEktBlQ+0Q96k4QjbPnrQEXlimPyXsBaZDOnaZctpnlJNo+wVKCyGjhBCyeXZ+vn3so/pTikX54sVG2r7gjoMHV7Wt+fD+/aursPh8rTHliuaRDbVFgXylhvmsjNO3y8MTp99wBE6VpaSctAXKze6PG/MDu0wdu0wdY34suyWZbDyUFkKGnXpd5qbMz7fzUwoFeSuX2/0pW7bIyRDSN6y2YnLex3fs/al7fZivCczZArlKA5lcCXOZ0lDlqVQdmZ/ygttI2y0/RQOwJaBh2tSwy+y+gJD0D5QWQoYRy2pXU9SmZFVRaTalpDA6fzRY1FCbqwNz7t6fTN7GfLaIbM6GMyQdtXZD4KQtReWULdCtoOLVgO0hDdOmDHoLsj9lYKC0EDIMNJvtYx9VTVGNtOrYJxqVG5NDIQa9DTua1m6oDQSQdxtqs7aDbLGMuUwR89nhaagt1KWkvGAtvd8noAM7TSkq24IafDp/BgYRSgshg0q53D72WVxNqVRkFSUa5bHPKBEMAqYJEQqh2NQwX3Mbaq0K5jKloWqozdYETriictad+KmcfgaBqTe0HhP2ANNhHdOmhi1d8lNOPv80du25dEOvm1wclBZCBgXHkUKyuJqi+lM0TUrK5KScBOGxz2gQCMg+lVColVA7XxAo2DXMZUuYyxRRrgz+gkI1mnzCcnDCcjC/qEc49+RXkf/+A9h09UH8p7ffiGlTw4ShLdlI+/ixB/HoQ1/EO657P6599wc24DsgawGlhZB+RlVTMpmF1ZTOkLdIBJie5rTPKKGi9EMhlDWPbKgtChQqNbmgMFtEyRr8hFohZG7KCUtWVXJLuFfgtWeQ//4DAIBXv3cfKnEdk9fetOSfq4QFAB575H7sff2bWHEZECgthPQTqjdFiYqSFFVRAWQ1hU20o4caUTZNVHWvPPqxBPLVOuazFuazwzH5I4TAa1WB50tSVIpLnGZtMjRMhzXsNnXEpn8JjxdvbomIur+mi7h0CgsAvOv6myksAwSlhZBeIoSc9MlkZLhbNivfV0c/rKaMNl5vS1TUiPJ8WSBXayDjikquUIYY8MkfFfZ2whI4UXJQ6jLyo0aTd4dlM23Yu/DYRwnKcuLSTVi6iQ3pXygthGw01WpbUFQKrZKUYlFWTyIRYHycvSmjSIeoNLw+ZGpy50++pkaUS8jmLTjO4IvKzyvtiordRVR0AFNBDXvCOnaFNIS8y0/8LCcuFJbhgNJCyHqjjnyUpBQKUlTU0U+9LuUkEpFNtIFAr6+YbDQq9M000fD7ka0JzFeBXLGJbN7GfNZCJj/4I8qOEDhTFnje7VHplkrrAbAtJI99dpmr3/HTTVye+O43YVvF1mMoLIMLpYWQtUYIKSNKUvL59pFPqSTfDgSkpGzdKvM0uNdn9PB4WlkqTcNAtgbM1wRyVhO5QgVz2SIyWQuNIRCV066ovFByUO7y7Xg0YLtbUdkZ0mBcZNjbYnGhsKwOn88Dw++F3+eV9+7bfp8HIa23FT5KCyEXi+pLWUpSSiX5AhUOA+k0sGOHPAIgo0enqLjptPM1gazdRK5YwXy2hEzWQr2xxGKcAWGlorIjpGGPqWOnqcG/xmFv11x70zkVlpAZobAA8Pu8CBheGH4fDEOKieH3tQTFq2swdLnZ2u/R4NcAQwd8ugZ/qQDDq8sKcg/gMychF4JltY98lKSo3pRSSWaqqHC3zZtlIi0ZTRaLSsOtqNgOcqUK5jMlZHIl1OqDLypnygLPLSMqXiUqYRmfv9ai0snjxx5cICyArLg8fuzBoRcXTdMQMHwIGF733gdD3fu98HmklBiunBiejrd1+feEZhNoNOR93b1vNoGXX5a/dF1+eU++N0oLISvBtrtLihKVRkNWUsJh2UAbCDAqf5RZJCr5hqqoSFHJZEuYz1oDn06rmmmfKy3do7KRoqJY3HQbMiMtgVluHHrQMPxeBAI+BAN+BA0fAoG2mBi6hoAHMDwaAjoQUO8rKWk02rdaY+H7y1VRLEv2X/UISgshixGiLSm53LmSUioBtVp7FJn7fAiwrKjkS/LoZ1hE5dUOUek29dMpKjtDG7vnZ6kpoc6PD5K4aBoQMPwIBV05CfgRDEhB8Xt0BD1SSIIeIOgKiuEBPELIJv9GA6jW20JSr/fsaGctoLQQIkR7uaC62XZ3SQmH2TxL2qipn1AITcNArgbM1+XRzzCJinBF5XlL4PmSA6vb1I8G7OyRqCiWG2teSY5LrwkYPoSCUkxCQXkLGD4EPG0p6bz3aZASUq/Laol6u16XR9RDCKWFjB7NZnuxYD7fjsTvrKY0GlJMKClkMV5vq6LS8PuRqwEZ1aNSLGM+ZyEzJKJytiorKs8vEfi23s20q2ElOSzrKS6rWb7o8eg48/LP8Etv+pWWnISCfhheHSFXSswOOfHCrZrUarJqosSkMdj/xi4ESgsZfqrVtpzk8+2kWSUpti1/K1GVlFSKxz1kIT5fW1S8PmTrcnlf3h1PzuSsoWimFUJgtgY8V3LwfMlBoctrospR2RuWomL0UFQUJ59/esXBcd3EZef0Gy4qyv/Yw1/BY4/c3/Xr+nwemCEDZtCAGfLDDBr45te/iL/9m7/Eh//gv+LWD38EIa+GkAfwa5BiUq8Ddq0tKgN8nLPWUFrIcOE4C5cKqqOexZKiUkc7A90oKaQTv78lKnWPtxX4li82kSuWkclayOQGfzwZkL03z5UcPFfqvpRQR1tUdq1Bjspas2vPpXjHde9fUhwW0yku77ju/RclLCeffxqPPXJ/688LBvy46X0fhBn0wwwZCPi9ML1AyKPB9AL/4+/+B/72b/4SAPA3n/8sbvyVX8KVb3hDu3pCloXSQgabSmXhQsFiUW5Gtix5s235mEBASkoqBWzbJl+QCFmMYbR6VKq6B5maQLYsI/SzBRuZnIVsbvAD3wAgWxN43pKiMl879/MagK1u4NvuC0im3WiuffcHVrWt+Zprb7qoCovHoyMcMvBrv/ZrKGU/gvv+7q8BAH//tS9geiKK//tD/wVhLxDQAc2tmBz53L247W/+pvVn3HXoEK7cuVM+T5EVMdTS8uKLL+Jzn/scfvjDH2J+fh6Tk5N45zvfiQ996EMIhUK9vjyyWhqNhXJSKEhBUVUUdQ+0XniwebO85/4e0g1Nk0IbCgGhEMrQZUXFEijUG8i5Efq5gj3wEfoAUKjL/pTnSg5muogKAEwFNOwJa9gd1hHqc1FZzGoFZKWP1zQgFPAjbAYQDgcQMQ2EAn6EPEDYq+HXP/FfsStu4La7/wIAcOSv/gKJuo3D73ufPN4RAkceeAC33ntv68+869AhHN6/f1XXS4ZYWn7yk5/gwIEDsG0bb3zjG7Fv3z786Ec/whe+8AU88cQT+NrXvoZwONzryyRL0Wy2M1CUpNh2u4qi7qtVufnYNIF4XEoKd/eQ5dC0lqQgGITlaMjUBDIlgWK1jkzeRg/dIWcAACAASURBVCZbQr5QhjPg25MBwGqoioqcAOrGpoCGvWHZUGueZynhKOD1ehAxDURcSQmHDAR9OiJeDWGvFBXTA+iNhnwOsmr4f69/D/yFXEtMbr3nHqBWw+H9+yksa8hQSkuj0cDHP/5x2LaNP/uzP8MNN9wAAKhUKvjYxz6G733ve/jMZz6D2267rcdXSgDICkpnUFuxKIWkUllYSalUFjREIpnkVA9ZGSpDJRiEEwig2NSQrQlkCgLFSh3ZnOxPKZTKGAJPQbkp8IIl8GzJwZmyQLdvadxoi0rUN9qiEjB8iIaloETDAVlVceVEiYofQgpKpSrvq9VzxoqViLTE5d578Rdf/zoyhULrMRSWi2MopeXRRx/FqVOn8Na3vrUlLAAQCATw6U9/GldffTW+8Y1v4CMf+QhisVgPr3QEqVYX5p+oxthOQVHvd7zQYNMm+TZ39pCVogQ3FELT70e+Lvs4snmBYrkqG2nzFkpWtddXuibUHIGTrqi8Ygt0O8xK+YG9YR17wzriIywqZshANBxAJBxANBxE0O9BxKsh4gUiPreKUq/L5yvbFZQVNskuFhcKy9oylK8A3/ve9wAAb3/728/5XCKRwFve8hY88cQT+Jd/+Rdcd911G315o4HjtAPaOvNPlJx03lQFJRiUt4kJ+WLj8/X6uyCDhmG0RKXu8SJbF8jWgLwlw94yOQvZvIVyZTimNBqOwIu2nPx50RZodimpxHzAJWEde0wdaWP0REXTlKQEEY0EETEDCPl1RL0aoq6kBHW4VZQKUOheRVkNh/fvP6fCkoxGKSxrwFBKy3PPPQcAuOSSS7p+fvfu3XjiiSfws5/9jNJysQghf9DVtI4SlHJZ/uAvFpRaTfacKEFJJOQ9KyjkQtA0+e/HrchVoLcmfgo1OZqczcmKSn3AM1QUTSHwiisqJy2BWhdRCXtURUXDuKFBG7Fx/rBpIBYJIhoOyp4UnzwCi7iiYmju81a5CmQrrWbZteLIAw8sEBZAVlyOPPAAxeUiGcpXipmZGQDAxMRE18+Pj48veBxZAUJ0n9SxbfkD31lBqVSksADyBSUQkNuOJybk2+xBIRdDx7GhCARQamqyolIUKNbqyOZtZPMWcnkbTWcIGlQgQ9/OVASeLQmcKDmodCkCBHVgjysqmwOjJSqhoB+xSBCxSBCRSBCmT0fMp8lqig/wCweolAHLrabUlhidWgMWN90mo9GWwKiPU1wunKGUFtudeQ8sMUWiPm5zNv5c6vWFvSXqpqoklUpbSpSoOI6UEVVBicfl28xCIWuFCnoLBs/pTymVa8jkLWTzNopD0kgLLIzRf26JfT9+HdhtytC3rUEN+oiIiuH3Ih4NIRaV1RTT70HUpyHmA6I+DYaSlJL7fLVBoW1LTQl1fpzicnEMpbR4PB44jnPe3zTEsDy7rZZG49xjGyUm1aq736K6UE6qVVltMQwpJIYBjI215WREnizJBqGOfdyjnyp0ZOsCOTc6P1+qIpuTolKurN9vzb1ApdM+W3SQ7xKj79WAXa6obA9p8I7Az57HoyMWCUpRiQRhBn2IeqWkxHwaguq4x6qseyVlKZYba+42VdT5cbJyhlJaTNNELpdDuVzu+vlKpQIACAaDG3lZG4fjLKyEqOpI59GNEhN1r261mmyANQx566yc+HyUE7J+eL0tSRGG0T72KQkUaw3kCzayORvZgo3GEETnd5Kvu6KyRDqtDrmYcG9Yxy6zNxuUN5qIGUAsKkUlYhqI+DTEfRpiPrmnR1c9c9mO4+gesZIcForL2jCU0jI+Po5cLofZ2Vls3br1nM+rXhbV2zJwqFG8xdUQ9bYaz6vVFspJ583rbYuJ3y8XBaq3BzA99snjx3Hlvn3r9niyTqgjxVAIDY8XuTqQqwvk3GMf1Z8yLPkpnajQt2eLAq9Vu39zU0ENlwxIjP7F4vd5EI+GEI/JakrY70HMlZSYD/DU6+50j/vLV5/8g3jy+PEVB8d1E5crLr2Uz0WrYCil5ZJLLsFzzz2HEydO4LLLLjvn8ydOnGg9rm8RAjh7Vja7Lq6GNBrt5VqdItL5vqZJAVG3YBCIxdrvD6CYLMUd992HO48eXXEGgvqt6PYDB3DHwYPrf4GkjcfTnvYJBGA5mpSUskCh3kShWEHW7U+pVIdjLLmTalPghJulcnqJ0LdJQ8MlYbnzZ5jTaTUNiISDiEeDiEdNREJ+RH0a4j4g7tMQgNuXUnCPsPt00/GV+/bh9gMHVvwc1Ckutx84QGFZJUMpLVdddRW+/e1v47vf/S5uvPHGBZ/LZrP493//d/h8PlxxxRU9usIVkMkAP/4xkM22BaVzTbnXK49rlISoCR11tDMiI8RPHj+OO48eBbCycmtnGffOo0fxtssv55PGeqJp7WPGYBANnw8FVU0pCJQqdWQLNnJ5G/lieSj2+yym3pGl8pIl0O2lV4W+XRKWUy/Dis+tpiRiIcQiIUQMGXIX98lgN11VjbPlnh/5rIY7Dh5c1XPJ4f37WWG5QIbyle3tb387Nm/ejCeffBJf/epX8bu/+7sAZC/LJz/5Sdi2jf379yOdTvf4SpdBNctmMkA6LY9vfL72jWPDAORvOXcdOrSic+Ju58580lgHVG+KO+5uORrydYFcRaBQbKJgVZHL28gVbFj24LwwrYamEDhly4rKC5ZAvUtJJeqVoW97w8Md+maGDCRiISRiJqKmgahPQ8KtphhwgLIN5MrtScQBZbXPJXzuuTCGUloCgQDuuusuHDp0CJ/61KfwD//wD5iamsJTTz2FmZkZ/MIv/AI+8YlP9PoyV4ZhAIPae7NBrKTBjQvL1hG1KVlVUzxe5BuympLPC5SqdeSK5ZaoDGM1BZDTiD93s1SeXyJLJeRRFRUNE0Ma+qbrGmKRIBIxE4lYCOGAF4lWEy2g12ruL2R2T6Z8yGAzlNICAG95y1vwzW9+E/fccw9+8IMf4MSJE5iamsINN9yAD37wg9zwPGQsJy4UlnVA9UkFgxB+P0qqmlIWKNabKJQqyLvHPlZ5eF+YhBCYrQHPFh08V3JQWiZL5ZKwjqkhzVLx+Tytako8GkTUpyPu15DwaTB1N5iyz3tTyGAwtNICAHv37sVnP/vZXl8G2SC4YXUd8Xrb1ZRAAFXospJSB/JlAatcQ64oJaVQLA9NEu1SZGvy6Oe5koNsl37hUchSCQZ8SMZNJGImYuEAoj4NSR8Q92vwO03AtoC83c54ImQNGGppIaMHN6yuEbq+QFIaHi8KDZknki8KlGoN5ItlWU0p2qhWu6SgDRnFhjz2ebYkMNNlRFkHsC0kKyq7TA3+IcxSCZsGkvEwknETkaAPCZ+GhN8dSa7VZEjlvL1hCbRk9KC0kKGDG1YvgM4pn0AAjt+PYgMo1AXy7pFP0aoiX7CRL5RRsisj8ctzWY0oFx2cqXT/hrcENOx1R5SDQ5alomlANBJEKh5GIhZCxO1PSfo1RDwCWqUCFGwe+5ANg9JChg5uWF0BKsfHlRTh98N2+1LyNaBoOSiVa8gXysgXbRRKlaFtoF1MzRE46WapvGILdPuux/3AJREde8I6IkOWpaLrGuLRkHv0E0LU8LRExdSFrKZkXVEZBXMlfQWlhQwV3LC6DGpvlLs7yhaarKTUgUJZwKrUUCiW5bFPsYx6fXR+c24IgZfdLJWTlkCjy2tx3CdHlC8J60j4h0tUPLqGeMxEKmHKRFq/jqQrKgE4sj9lzpIZKoT0kFVJy/79+3Hbbbfh9a9//XpdDyEXDDesdqAqKR2SUnYlpdAACnkBq1qXUz5FGew2Cn0pnThC4HRZisoJS6DapaQSViPKER1jfgzViLLHoyMZM5FMmEhEQ4j6NaT8UlT8ThOwSkDOHqiQNzL8rEpannrqKdxwww1473vfi49+9KOIx+PrdV2ErIqR37CqelI6KykOUOyQFLvWQKEkqyiFYhnlyug1SwohcLYqs1SeKzmwuxSTAjqwO6zjdWENmwPDlaXi8ehIxk2k4qbc8+NKStKvwddsyLUhzE8hfcyqpOV973sfHnzwQTz44IP4zne+g49+9KP4nd/5naH6oSaDx0huWNX1BZIi/H7YTaDQECjWgULZgV1rotiSlArKldF9IZqrSkl5ruQg36Wg5HNHlC8J69gW0uAZouc0VVFRRz9xv46UD0j4NfgadXfix+LEDxkIViUtt912G2688Ub8yZ/8CX74wx/iU5/6FL7xjW/gj//4j3H55Zev1zUSsiQjs2FV5aS4m7kdnw+lhhzDLdaAou3ArjZQKJZRLFWQL5aHcuHgasjXpag8W3Iw38XXPAB2uFkqO0MafEM0ouzx6EjEQkgnwq2Kijr68TbqsqLC0WQygKy6Efd1r3sdvvrVr+If//Efcffdd+OnP/0p3v/+9+O3fuu38IlPfALjjJwnG8hQblhV/SiqkmIYaGg6ikpSKgKlkgOrXEOxVEGhJEWlWhutnpRuWA1VURF4rUuWigZgKigrKrtNDcYQjSjruoZEzEQ6GUYiGkKsQ1R8FBUyJFzw9NBv//Zv421vexvuuecefOUrX8G3v/1tPP7447jllltw4MABeEdkyzDpPQO/YdXrbVVQYBgQPh8qQpOC0gBKRQGr0UTJrqJYqqDoSkpjREaQz0dFZamUHJwpC3Qbwt1kaNgb0bDH1GEO0YiyrmmIx0JIJcJIxN2jH1dWePRD1pR6XU6PVauAafbsMi7KLEzTxOHDh3HDDTfgT//0T/Gv//qvuPvuu/H3f//3+OQnP4krr7xyra6TkGUZmA2rqmG249bQdJSaQKkhUKoBRVugXGugWKqgZFXkvV2FYCZGC5Wl8lzJwctLZKmk/Wo5oY6ob3hERdOAWCSEVDKMZMxE3NCRMqSo+FUzLUWFXChCyEZs283iKXfsjFIp2aYpf9nqAWvyVaenp/GlL30J3/3ud3HkyBG8+OKL+P3f/31cffXVuPXWW7F169a1+DKEDBbqmEcd9fj9cHw+lJWguFUUu9mEZVdRtKotSeFRz7moLJVniw5etLtnqcS8MvRtb1hWHIaJSDiAdDKMVDyMaMCDtFtRCQh3PDljceqHrA4hZOWkU1BsWz53BYNAKAQkk/Jtw5Dvh8NANAr0qBVkTVXp6quvRiwWwyc/+UmcOXMG3/ve9/Dkk0/i937v93Do0CEYhrGWX46Q/kHTAJ+vJSfw+yH8flQcwGq4klIRsEsO7GodJVdQSlYVll2FwypKVxwhcKosj35esARqS2Sp7Anr2BvWMGEM14hyKOhHOhlGOhlBNOCVomJoCMFxc1Qs5qiQlaMERUmKbctJxFBIisnYWCslG6YJRCJSUsJh+b7H0+vv4OKk5dSpU/jxj3+M//iP/8BPfvIT/OxnP0O9oyQphEC1WsXf/u3f4uGHH8anPvUpvPWtb73oiyakp3RWUDpuLUFpClhVAct2UKk1pZzYVXmzqmg0Ridp9kIQQuDnFYHnSnJBYbmLqKgslUvCGrYMWZaK4fcinYwgnQwjFvIj6deQNjREVIT+bInJtOT8NNyjwnJZ3tu2/HgoJG9KUILBtphEIvIWCsnnuT5kVdLy/e9/Hz/+8Y/xk5/8BD/+8Y+Ry+Van1Pn7R6PB3v37sVll12GN73pTQgEAvjsZz+L5557Dh/84Adxyy234I/+6I/W9rsgZL3weM6RE+H1ouwKitUQsJWg1Juw3MpJyZb3POZZGULIzcnPuqJS6uJ1/o4sla1DlqXi9ehIJcJIJ8OIR4ItUYl6BPRyWR79cNcPWQohFsqJ5fY0qf6TRAKYmmoLipKTPheUbqxKWj74wQ9C07QFDYGRSARvfOMbcdlll+Gyyy7DL/7iLyIUCi34766++mp8+ctfxt13343Pfe5z2Lx5M66//vq1+Q4IWQvU8Y6SE/ftpq7DbgJ2Q8BqApYtUG46qNQasOwqrHJN3lNQVo0QAnM14PllQt88GrArJLNUdoQ0eIcoS0XXNCTiIaSTESTd0Le0X0PCB3iqFSDvvgA5nBIji1BVlE5J8fmkoKgqSiDQ7j+JROS9acrjoAFm1cdDU1NTrSrKZZddhj179py3NKvrOg4ePIh0Oo1PfOIT+OpXv0ppIb1B02TXe4eYwOeD8HpRcYBy062eNAC7KlBpNlGu1GErOSlXYds11HnEsypOPv80du25FACQrbXTaTNdBlx0ALHZ/w9vfsM+7DI1+IdIVAAgGgm2GmrjAb3VUOur19ovRE3++yIdVCrtfxuW23AdCkkJGRsDtm+XVZRodOFtCKNHVn08lEqlLviLXXfddbjjjjtw8uTJC/4zCFkRqnKibkpSvF5UHcBuAuWmkPeqelJvwi5XYZdrrVu5XGOT7EVy7OGv4LFH7scvvfP/gveX/zNmuwy4qNC3vWEdZ578Jr77rS9i/Lr343Xv/sCGX+96EAz4MJaMIJUMIx70IW1oSKvJn1KRI8qkjTrqKZWkoJRK8uOqGTaVah/zxGJSTmIx+bEBOua5UFYlLRcjLIpoNIpXX331ov8cQgDI3yQ65cR9X3g8rcpJuSnkvSsntUYTdqWOshKTSg1WucYG2TWm2BD4/vHjeOyR+wEA//GdLyFuC8R+9YbWYzYHNOwNa9jthr49fuxBfPdbXwQAPPbI/dj7+je1KjSDhtfrQToZxlgyjHg4gFRnQ61lAbkSJ3+IPP6z7bakWJZ8HlNHO5s2yaqKqp4oUfH5en3lPWHDa0e33347fvSjH230lyWDijrOUXLSee/1oiaASlOmopYdoNIAylWBqiP7TiqVOsqVGsruvV2poV6nnKwXVkPghCVj9H9eEUD09YhfdRC5f74PAJD75/sQ9gK//n/ciD1hHZGOdNrHjz2IRx/6Yuv9d11/88AJi6ZpSHb0qST8OsYMDXEf3IbaEhtqR51OSVGi4vdLSUkmga1bpaTEYvIWj8vPDXgvylqx4dJy1VVX4aqrrtroL0v6GSUlXW7C40FNANUmUHGEKyhApSZQaTqoNx1UqnWUK3VUqnVUKnXYlRoq1TqajLnfEMpNgRPuvp8zlXNj9GO/egNMD3Dme/cBAE4/fh+yMR2Ra29qPaabsFzT8fl+J2waGE9F5SZlw4MxN6HWW68BRfeFiQ21o0k3STEMKSLptOxHMc22oMRi8v0ROOq5EIavS4f0Fx6PvHm97fvOtz0e1AVQdYCaIysmVQeo1oFKRVZM6g0pJtVaW0wqVXmrsWrSE8pNgRcsOZ58aol9P0mfCn3TkZzej8fjektM1P011940sMKi8lTGUhHEQj6Mucc/QfapjDaqJ6VYbEuKzycneNJpYMcOWUmJx9u3RRO3ZGkoLeTCUDKy1M0VkiakjNQcoOqI9tt1oKakxHFQqzVQrTZQrTVcQXHvq3UuBuwTKotEpdvfSswH7DVVjD4WTBYqEekUlye++03YVrH1mH4XFl3XkIqHMZaKIBGVeSpjbp6KxuC30aVSaUtKqSSfA8NhmY+ybZuUkkSCkrIGUFqILEPquvxB0/WFbysJWfR2E0DdFZC6AOodQlKrCdSrQM1x0HAEavUmarUGanUpJZ1vV6sNjg/3MdWmwElbjii/ssRiwqi3XVEZWyQqi1ksLoMiLNFwAGOpiNymbMg+lYRPg7dakQ21ts0+lVGiXm9LSrEoj4BUFsrmzfJ4RwlKItHTrcjDBqVlkNG0tnAsda9ui9/vEBMBoCmAhnurO3I5nbx3paQBNGrCFRQHTSFQrzdRbzRRqzdRrzeknNQbqLv3Uk4oJIOGEpXnXVHp9jcY8QJ7TLnvZ3yV+36uufamcyosITPSd8Ji+L0YS0UwlnSPf9SYstNo/0bNPJXRwHHkMU+hIP/eK5V2suzY2MKelERCfpw9KesCpaWf2bJFnoGOj7cFpVNUIBfKNYWUDkcATbTfbgjh3qP1mIYDNBuiJShN4aAhAMcRaDSaaDQdNBpSRhoNx72X7ytJUfdkeFiJqKzVYsLHjz24QFgAWXF5/NiDPRcXXdeQjJsYT0Vbxz/jhoaI7kCzOaY8Uqi+FFVRUQmzqpISjUpBSSalsHC6Z0OgtPQrXi8KwQhONQIQZQ8cSBGR9wKOaMKBrEg7woHTFGg6DhxHoNl05M2R9w31fsfbSk6a6t5haXvU6BSVl5c4+jFdUdkT1rBpDTYoL266DZmRlsB0NuduNGr6J50MI+4e/yR5/DNaNJtSUAoFeS+ErJiovhTVo5JMyvsRzUnpNZSWPqYhgFcLVbzycg6OI6SsKDFx2m8TslJUM+0Ja+kelZaomBo2reEG5aWmhDo/vpHi4vN5MOZO/8RNP8bcptrW8Y9lyR0vZDhRUz5KUmy7HeKmjnzi8baksC+lL6C09Dn1egP5YrnXl0EGGDWefGKZqZ/1EhXFcmPN3aaKOj++lmgakIiZGEvJ8LeUW1WJcfpnNGg225JSKMh/EKovRW09TiblLR7nkU8fQmkhZAixGgInLQfPWwKnl8hRCXuA3esoKoqV5LCst7gEA36MpyNIJyNIBDytplpvrQrk3aoKj3+Gk85qimXJikkkAkxPLzzySSZl3wrpaygthAwJpYbAC5aD590I/a6i4k797AlrmFyDHpXzcfL5p1ccHNdNXHZOv+GCo/w9uoZUMiybaiMBpN3jH1Nz3PC3EsPfhhHHkcd7hYK8OY488kmngZ07pbCkUmygHVAoLYQMMIW67E85URJ4tdq9UqByVHabFzf1cyHs2nMp3nHd+/HYI/evKIelU1zecd37L0hYIuEAxlNyo3LS8GDcryHhB3TblqJS5nHr0FGvtyWlWJQx+dGojMiPRORRjxKVYLDXV0suAkoLIQNGpiZF5YWSg5la98fEfbKisnsFgW/rzbXv/sCqtjVfc+1Nq66w+LwejKUiGE9HEAv5MW5oGPNrMJp1+Vv3jMVMlWGjXAbyeXmrVKScxGIyKkJVU1IpKSweT6+vlqwRlBZC+hwhBGZrwAuWgxMlB5klTjRSfmC3qWO3eW6Efq9ZbcVkpY9PxEIYS0WRisum2nEVqW8xU2Xo6Dz2yeflx6JRYHJyYTUllZK9KmQoobQQ0ocIIfBqReCEJftUCktM3o77ZTPtblNHwt8/krKeGIYX46moHFUOeltVFTbVDiHNZrua0nnso3pTEom2qPj9vb5asgFQWgjpE5pC4FRZjieftBzYS5xmbApo2G1q2G3qiPpGQ1Q0TSbVTqRlUm3akEm1YTbVDh+1WltU1LSPOvYJh2VDbSolhYVNtCMHpYWQHlJzBF62ZY/KS7ZcOrkYHcBUUMO0qWHa1GF6R0NUgPao8lhKjiqPdybVZtxAMDL4dPanVKuympJKyYqKmvxJp6W09NGxJ9l4KC2EbDB2Q8bnv2DJsLdml5MMjwZsD2rYHdaxM6Qh4BmdJ2pd15BOhDGebo8qjwc0hERTVlVmS0yqHXSEkFUUJSqOI6spmza1j31URYXTPqQDSgshG0CuLiXlBUv2qnTD0IGdIVlN2R7S4NNHR1QAwAwZmEjL/T8JQ8e4oSOpRpXnOKo88KhG2lxONtPquhSVbdva0z5KVLjXhywBpYWQdUAIgbPVdn/KUhM/pgeYNnVMmxq2BDV4Rqz07fHoSCfCmBiLIm4aGHN7VQJOAyjmOao86KglhPm8FBW/X4rK9PRCUUkmOZZMVgSlhZA1ouHIRtqTtsCLlgNridfapA/Y5YrKRoe99Qth08C4W1VJGbJXJe4VsqrC/T+DTefET6Egj3fi8fZocjotd/3E4+xPIauG0kLIRVBuCrzk9qe8YgvUl5i03WRo2OU20o7KaPJiPB4dY8mI7FUJy63K40ZHAFypJI8QyODRaLRFpVSS25LVxI/ampxOy7cpKuQioLQQsgqEEMjWgRctBydt2Z/SzVM8GrAtqGGXKRtpR2niZzERM4DxsSjSCRNJw4MJt6qi2TYwU2QA3KBSr0tJyeVkU204LKsn27a1RWVsjEFvZE2htBByHppCLiB80RI4aTvIL9GfEtSBHW41ZVtw9BppO/F6dKRTEUyko4ibbqy+ocFo1NvbdllVGTzqdSkp+bwcNw+HZT/Kzp2ysqIqKqbZ6yslQwqlhZAulJsyP+VFe+n8FABIuP0pO0MaNgU06CNe+o6EA5hIR5FKmAt6VRirP8B0ioplySqKEpV4vF1R4Wgy2QAoLYRAHvvM14AXbQcv2gKvLXHsowHYHJD9KTtDo9uf0onXo7vLCttVlXFDg19VVUolxuoPGkpUcjlZUekMe0sk2qISCPT6SsmIQWkhI0vdEThdFnjRFnjJdlBcIq/M0IHtIQ27QjI/ZZSC3pZj2apKtijj2Mng0K2ioppnKSqkT6C0kJEiX5eC8pItlkyjBeRY8k4e+5yDx62qTLCqMhwsbqZdXFEZH5eiYhi9vlJCAFBayJDTEAI/L8ux5JdsB9klmmg9ALYENewMadhh6oiPyCLClRI2DUyMxc6dAGJVZfBoNBYe/UQi7R4VVlRIn0NpIUNHwa2mvOxWU5bKTjE9wI6Qhp2mjq1BDf4RnvbphsejI50My83KKq02wAmggUQFvmWz7fHkzmZaVVGhqJA+h9JCBp6GI3CmIqd9lqumaAAmA5oUlZCOtB8jmUZ7Plo7gFJd0mrPMldlYFCikstJyVQ5Kjt2yPFkJSqc+iEDBKWFDBwq4O1lt5pyurJ0b0rQA+wIyiOfbUE20S6FrmtuVSWGRNho5aoEmqyqDBSOI6Pzs1n59xYKtQPfOkUlFOr1lRJyQVBayEBQacqjnldsBy+XxZKTPp3VlO0hHeOspixLKOjHRDqKsVQECUPHREBHQlVVmFY7GDiOFBQ1+RMIyN6UqSnZWDs+Lm8MfCNDAKWF9CVNIXC2IvByWeAVW25MXmomJeyRI8nbQ7I3hdWU5dE1DcmEiYmxGJKRAMYMubixtVmZO4D6HyHk31M2K0XF75cVlU2bn1lKLwAAIABJREFUFooKI/TJkEFpIX2BEAK5OvBKWS4ePF0WqC1hKR4N2BLQsD2kYVtQR4rVlBURMHyYGJNVlWTAgwlDR9IPd7NykZuVBwHLkhWVbBbweGRFZc+ehaISjfb6KglZNygtpGdYDXnkc6rs4JWyQGmJIx8ASPmArW6425bAaO/1WQ2aBiTjJibSMSRjQaT9GiYCGkKiCRRzwExJNmyS/qVclpKSy8n3YzFgelqOKo+NSVGJx7k9mYwElBayYVQdgTPltqjMLxPtEdSBrSEN24M6toU0hEd4S/KFYPi9GE9HMZ6KIBH0YiKgIeXT4KmUgbmifCEk/UutBmQyUlTqdVlRUc206bQUlUQC0PVeXykhGwqlhawbDUfg1ao86jllC7y2TF+KOvLZFtSwjePIF0w8FpLjyvEQUoaOSUODiSZQKsrGWlZV+hcVo5/NyqO6eBzYvFmKSiolRSWVksdChIwolBayZjSFbJg97VZTXl1mFBkAxg1XUoIyKt/LI58Lwuf1yKpKOoJEyIcJQ0Pa0OCtVIBMUaaekv5kcehbJCLlJBaT4W9qRNnLp2pCgBGSlptvvhlPPfUUnnrqqV5fytDQFAKzrqScLgv8vLJ0+iwAJHzA1qCc8JnilM9FE40EZVUlYSJl6JgwNER1R1ZV5ooyrp30H2pEOZNpZ6kkEjL0Te37GR+XE0GEkAWMhLQcOXIE3//+9xFioNJF0RQCM1XZl7ISSYl4ga1BDVuDOqaC7EtZCzoXFiY6Fhb6alUg51ZVuLCw/+g2opxMyiyVWAyYmJCiwnRaQpZlqKXFtm3ceeed+Na3vtXrSxlIGo487jlTkZLyakWgsczroekBpoIaplxJiXnZl7JWmCFDjisnw0gaHkwaGmJcWNj/2HZ78kfXZSVl7972iPLEBLNUCFkFQyktQggcO3YMn/nMZ/DKK69g69atOHXqVK8vq++pOVJMfl6R1ZTXqsv3pJgeuRl5KqhjKqAh7qOkrCW6piGVDGNyLIpEONCqqhgqWr9UYlWlH6lWpahks7JnJZGQiwmjUdmfMjEhqyv8WSFk1QyltJw5cwYf/ehH4fV6cfPNN+OGG27Ab/7mb/b6svoOqyEF5ecVgZ+XHczWsOR0DyCTZ7cENWyhpKwrKgRuvCMELuFjtH5f02i0RaValVKiYvTTaSkqySRHlAm5SIZSWnw+H66//nocOnQIO3fuxOnTp3t9ST1HLRmUkuLg5xWB/BLbkBUxL7A5qGFLQB73RHncs24sDoEbc0PggozW7186tyiXSudO/kxMSGHh5A8ha8ZQ/jRNTEzgz//8z3t9GT2l7vajqOOe1yoClfO85qX8wOaAji0BDZuDGiJsnF13/D4vxtNuY23QiwlDQ8rPELi+RQh5NKcaatUW5e3b5b1qqOXkDyHrQt9Ly4c+9CH80z/904oe+/jjj2Nqamp9L6gPEUKg0ABeq8gwt1crAnNVgeUcxQNgPKBhc8eNI8hrx8nnn8auPZcu+flYJIiJsRjSiRDSfh0vPP2/se9XLgeKBbkHiCFw/YVqqM1mZeUkkZDLCWOxdkMtpxMJWXf6XlpSqRS2bNmyosd6R6QMW3OrKK+5FZTXqgL2eV7jgjqwKSBD3DYHZEMnw9zWh2MPfwWPPXI/3nX9zbjm2ptaH/eqceWxGBIhX6ux9r997h7c+pnP4PYDB3DHwYO9u3CykM6GWseRlZTp6YWTP1xOSMiG0vev8p/+9Kd7fQk9RQW4SUlx8FpVIHOehllALhjcFNAwGdCxmU2zG8bJ55/GY4/cDwB49KEvAgB++z//nzIELhlGyvBgMiBD4DSrhCOf/Txu/cIXAAB3Hj2Kt11+Oa7ct69n1z/yLNdQqyZ/kklO/hDSI/peWkaVh56ZxZf/1xk8M19B/Ty9KIYOTBoaJt1KyqShweBRT0/YtedSvOv6m1vC8uhDX8TOqRT+nw/9F4wHNBj1GpAvApaFI1/7Gm69997Wf3vXoUMUll7QbAKFghSVYrFdSVE7f1RDLXf+ENJzKC19yGyxio//zxe6fk4DMOYHJgJ6S1QSrKL0DQHDh5t/7xZs3ZTAFz733wAA93z2LzGl13H4xhtb48pHHnjgHGE5vH9/T655JOlMqM3lZBKt2qSsovQnJthQS0ifQWnpQ6JBL944aeInr1lIGTpSPoEJQ8OEimxnL0pfoWlAImZicqw9rvzOj/0hdgQ13Hr33QCAW//7fwdsG4f376ew9JJyWe786Uyofd3rZHVlYoINtYT0OZSWPsTwevDwB/bhzCtn8ZMzBfzs1UKvL4l0we9T25WjSHYZVz78rncBhUJLUG699178xde/jkyh/fdJYdkAajUpKZmM7FnpTKjtbKhltZKQvofS0scEvUzP7EfkuHIUqbiJtKFjMqAhrDldx5WVkChxobBsECr4LZOR48rRqBxRjsdln8rkJBNqCRlAKC2ErAC1XXlyLIp4yN86qvPWqnJhoWUt+d8e3r//nApLMhqlsKw1QrQbagsFecyTTMqqimqoHRtjQi0hA8xI/PROTU3h2Wef7fVlkAGkc7tyyvBgwtAQ88hxZWSKQP08uxAgm247hQWQFZcjDzxAcVkLLKs9puz3y+OfzZvbCbUTE0Ag0OurJISsASMhLYSsBl3TkEqEMTEWRTJycduVFzfdJqPRlsCoj1NcLoDFwW+JBLB798KE2kik11dJCFljKC2EuKjtymMd25WTF7Fdeakpoc6PU1xWQaMhG2qzWTkFFI/L4LdYrB38lkiwoZaQIYbSQkaeRCzkjiuHMOaOlofQBIo5WVm5gO3Ky401L27Opbgsg+Ms7FOJRGTQm2qoZfAbISMFpYWMJD6vGleOIBHyYdIdV/ZWysD8xW1XXkkOC8VlGYRo96nkcoBhyArK1q0LNykbRq+vlBCywVBayEgRDQfc7comUoaOCUPuAUKpCMwV5RHERfDk8eMrDo7rJi5XXHrp6Eb5VyrtPhVAisqePfL4RzXUmmZvr5EQ0lMoLWTo8Xh0pJNhTI7FEDfb48q+WhXIFWWOxwoba8/Hlfv24fYDB3Dn0aMrymHpFJfbDxwYPWGp19vBb7WarKRs27awTyUeZ58KIQQApYUMMaGg3x1XjiAVkOPKca+AZlkyW6VWW5eve8fBg6va1nx4//7RqrB0LigslWSfyuSkDIBLp6WopFLsUyGEnAOlhQwVmqYhlTAxMRZDMhJoNdYG1LiyZV1QY+1qWa2ADL2wLLWgcPt2WUmZnJSVFS4oJIQsA6WFDAWG34uJsSjGU1EkgmpcGfCUbRmtX6n0+hJHk3K53afCBYWEkIuE0kIGmngshMl0FKl4CGm3sdZU48ql0oI9QGSDUAsKs1n5diIB7NixMPiNCwoJIRcApYUMHF6vBxPpCMbTUSRCPkwYGtKGBm+lIqP1bbvXlzh6dC4otCwpKJOT8r6zT4ULCgkhFwGlhQwMkXAAk2MxuV05sPbjymSVCCH7hFTwWzDYXlCYTLYXFPp8vb5SQsiQQGkhfY1H15BORTCRjiER7hhXrteAXGFNx5XJCrHtdp+K1yuPfzZtaldXxselwBBCyBpDaSF9SSjox+RYDOlkeEPHlckS1Gry6CeblUdBiQQwPS17Uzr7VAghZB2htJC+QY0rT47FkOjYrrzR48rEpdlsV1Q6FxRGo+3gt2SSDbWEkA2D0kJ6TsDwtfYAtbYr+yG3K3NceWNxHCmImYy8N03ZQNvZUJtOy2MhQgjZYPjMQ3pGMm5iIh3tvl15huPKG8biBYV+v6ygTE21g9+4oJAQ0gdQWsiG4vep7cpRJIJeTKzhdmWySpZbUKj6VMLh3l4jIYR0QGkhG0IsEpTbleMhuV05oCGicVx5w+GCQkLIAENpIeuG1+vBeCqCiXQU8ZCv1VjrrVXlBJBl9foSRwMV/JbNyv/nXFBICBlQKC1kzYmYAUyMRZFOhFtVlZjHXZiXKcrf9sn60hn8ls/L/T4qTj+RkKIyPs7gN0LIQEFpIWuCx6MjnQy3QuBUVcVfrwF5t6rCELj1Z7ngN7WgkMFvhJABhdJCLgozZGAiHUU6FUbKYAhcT6hWpaRkMlIM43EGvxFChhJKC1k1uq51VFWMVlXFYAjcxtFotCsq1aqspGzdyuA3QshQQ2khKyYU9GMiHcVYKoKEoWMioCPhFTIEbqYoXzz///buPSqK8wwD+LPAchERWC6iEg1ahhBUjKbaKiYqals1qdr2mCZGbUVJ4iW10iLHRIQTEiBpavEWTxNrNdYYkkpDz7GYBE1LbBKLCdZoQUGjWKICi6KwuOxO/5jOLquL4TJ7meX5ncOJ2VnHdz5Z5+Gbb94hxzGZpAcT6vXS+qCgIGkmJThYWkgrN37jgloi8lAMLXRXXhoNwkL7Y2DEAIQG+VuawPmb24Hma9LJk7MqjnP7gtqAAGmdytChtgtqfX1dXSkRkcMxtJBdAf5aDAwPRkRYf4Sytb7zdbagdsAA64Lafv1cXSURkVMxtJCFl0YDXajUWj90QAAifDUY6K9BgLkduHGdrfUd7ZsW1MqXgoiI+iiGFkKAv/TAwogw6YGFkX5e0GkB79YWoP4GW+s7ktyhtuOC2qFDbRu/cUEtEREAhpY+S6PRICw0EJHhA6D7/6xKpL8G/cT/P7DwBmdVHMZeh1r5tmQuqCUi6hRDSx9z56yKBjqtBt6GVukZQJxVcQyz2bqg9vp1+x1qIyK4oJaI6C4YWvoAea2KPKsS7ivdAdQPJqD5OmdVHEUUpZkUvV66BOTrKwWUwYOl9Spy4zd2qCUi6hKGFg8W4O9r6VZ7x6xKA2dVHKa1VVpM29QkrUUJDQViY2071AYFubpKIiLVYWjxMHJflciIAdAF+SPcZq0KZ1UcRr7zR6+Xxle+9BMcLF32iYyUZle4oJaIqMcYWjxEYICvZa1KqJ8XIv28EMo7gBzL3p0/0dHWO38iI6WFtV5erq6UiMgjMLSomLeXBuG6IESGByGkv9StNtKvQ18Vzqooz96dP3L/FJ3OeuePDz9aRERK47+sKtQ/0A+R4QMQrusPnZ+0ViXUR4RXayu71TqC2Wx95k9zs3Tnj05nvfNHbvzGO3+IiByKoUUlfLy9EBEWhMjwAQgJ9EWErwYRlmcANfMZQEqTn/nT1CTNrPj5SQElOlqaVZGf+cM7f4iInIahxc35+WkRGzMQYSGB0Pl5IdJPgxAfERo+WVl58i3KTU3Sl4+PtHhWEKzP/ImMBPr3d3WlRER9EkOLm9MF+uK+0ECE+2nga7wFNN+QTqycVVFOa6u1lwpg/5k/AwZ06c6fsrIyJCUldfmP7u77iYj6Mt7W4K7MZoT4AGO0Bgw23oDv13VAXZ10yYKBpffa2oCvvwZOnwaqq6UxHTYMGDUKeOABYMIEYOJEqb9KcHCXAsvGjRsxefJk5OXldamEvLw8TJ48GRs3buzlwRAR9Q2caXFXZjO8aqqBy5eB4cNdXY1nuHXLeovyrVuK3qJcVlaGrKwsAMC6desAAOnp6Z2+Py8vz/K+rKwsTJ8+nTMuRETfgKHFnRmN0joL6rn2dmtQaW2VAkpUlPXhhJGRityinJSUhNzcXEsQuVtw6RhYACA3N5eBhYioCxhayPPY66USHi4FFZ3Ouk5Fq1X0j5UDyt2Ci73AcrcZGSIismJoIc9gMkm9VJqarL1U5Fb68sMJIyOlW5cd6G7BhYGFiKh3GFpIvcxmKaDo9VJgCQiQAkp0tG1QcXIvFXvBJT8/H42NjZb3MLAQEXUfQwupy+1N33x9pRmVwYOlhbVyUAkMdGmZtwcXBhYiot5jaCH3J4pSx1+93hpUOjZ9k4NKUJCrK7WRnp5+xwyLTqdjYCEi6iGGFnJPt3en9faWZlRiY6WgEhHRraZvrpCXl2cTWABpxiUvL4/BhYioBxhayL10DCoajW13WrmXSkiI2wYV2e2LbnU6nSXAdKWPCxER3Ykdccn1WlqAS5eAU6eAr76SXouJAUaPBsaOtXanjYuTZltUFlhyc3PR0NCA3Nxcy2vr1q3rcudcIiKScKaFXKPj835EUZo9GTbMOqMSESH1VOlBd1pXutttzV3p40JERJ1jaCHnaW21dqc1m6WgMnSobXfaHrbRdwdd6cPC4EJE1HMMLeRYra3W7rQmk3Rb8tCh0p0+HYOKt7erK+2VsrKyLjeOsxdcJk2axFb+RETfgKGFlCcHlaYm6flJcsM3eUYlIkK6BKTyoNJRUlISMjMzkZWV1aU+LB2DS2ZmJgMLEVEXMLSQMm4PKsHBwJAhts/7CQvr9YMJ3dnGjRu79bTm9PR0zrAQEXWD555ByPE6CyrypR95RsWDg8rtuhtAGFiIiLqu75xNSBkMKkRE5CI8s9A3k+/6aWoC2tulNSoMKkRE5GQee5apqqrC66+/js8++wz19fXw9/dHfHw8FixYgDlz5ri6PPfXMajId/3Ii2l1OgYVIiJyOo8845SWlmL16tUwGo0YNmwYHnroITQ0NOBf//oXPvvsM3zyySd44YUXXF2m+2lpsQYVuY/KPffYzqh4+GJaIiJyXx539mlubkZGRgaMRiN+/etf4+c//zk0/2/7XlFRgaVLl6KwsBATJ07ErFmzXFyti4miNahcu2btTHt7HxWdjkGFiIhcTp2tR+/i/fffR1NTE8aPH4+lS5daAgsAJCYm4qmnngIAvPfee64q0bVEEbhxA6ittX3Wz7Bh0rN+xowBxo8HkpKAkSOl0MLAQkREbsDjzkZGoxEJCQmYMmWK3e3Dhw8HAFy5csWJVbmYHFTkGRUvL2lGJSbG9tKPTudRDd+IiMizeFxoWbBgARYsWNDp9oqKCgBAVFSUs0pyDbMZaG6WQsq1a4BWKwWVESOkoCI/lDA0VLXP+iEior7F40LL3Vy+fBl79uwBAM9cz2IySUGlqQm4fh3w85OCSmysbVAJCWFQISIi1XH70JKamoojR4506b0ffvghoqOj7W5rbm7GM888g5s3b+Lb3/42Zs+erWCVLmQyWWdTmpuBgAAplAwebBtUgoOBDut7iIiI1MbtQ0tYWBiGDBnSpff6dLJgtKGhAcuWLcOXX36J6OhobNq0yWaBruoYjdautDdvAoGBtg8llINKUBCDChEReQy3Dy0vvvhir35/VVUVnn76adTW1iImJgZ/+MMfEB4erlB1TtTWZp1RaWmxNnmLiZF+LTd769/f1ZUSERE5hNuHlt746KOPsGbNGty8eRNjx47Ftm3bEBoa6uqyusdgACorgVu3rOEkKEhaQCvPqAQEuLpKIiIih/PY0LJ//35kZWXBZDLh0UcfRU5ODnx9fV1dVvf4+EhBJThY+q8cVMLDpUW2REREfYhHhpaioiJkZmZCFEWsWrUKK1eudHVJ3RccDAwaBNx7rxRSwsKk25aJiIj6KI8LLTU1NeoPLADg7w+MG+fqKoiIiNyGx4WWrVu3wmAwQKvV4ty5c0hLS7P7vkGDBmHt2rVOro6IiIh6yuNCi9zTxWg04q9//Wun74uNjWVoISIiUhGPCy3l5eWuLoGIiIgcgL3ciYiISBUYWoiIiEgVGFqIiIhIFRhaiIiISBUYWoiIiEgVGFqIiIhIFRhaiIiISBU8rk+LK9TW1gIAqqurMX/+fBdXQ0REpB7V1dUArOfSu2FoUUBbWxsAwGAw4Msvv3RxNUREROojn0vvhqFFATqdDo2NjfDz80N0dLSryyEiIlKN2tpatLW1QafTfeN7NaIoik6oiYiIiKhXuBCXiIiIVIGhhYiIiFSBoYWIiIhUgaGFiIiIVIGhhYiIiFSBoYWIiIhUgaGFiIiIVIGhhYiIiFSBoYWIiIhUgaGFiIiIVIGhhYiIiFSBoYWIiIhUgaGFiIiIVIGhhYiIiFSBoYWIiIhUwcfVBfQV586dw9atW1FeXo6GhgZERUXhBz/4AVJTU9GvX79u7evy5cvYtm0bjh49iq+//hrh4eGYNm0aVqxYAZ1O56AjcD9KjumRI0fw5ptv4uTJk2hubkZISAjGjh2LlJQUJCYmOugI3IuS43m7vLw87Ny5EytXrsSqVasUqtj9KTmmLS0t2LlzJ0pKSnDhwgV4eXkhPj4eixYtwve//30HHYF7UXI8v/jiC+zYsQPHjx/HzZs3ERYWhokTJ+Lpp5/G0KFDHXQE7u38+fOYO3cu5s+fjw0bNnTr9zrrvKQRRVFUbG9k14kTJ7B48WK0tLRg9OjRGDRoEI4fP46rV68iLi4Of/rTn9C/f/8u7evixYv46U9/iqtXr0IQBMTExODUqVO4ePEioqKisH//fkRFRTn4iFxPyTF99dVXsWPHDmg0GiQkJCAqKgo1NTWoqamBt7c3cnJyMG/ePAcfkWspOZ63+/jjj7F06VKIotinQouSY1pfX4/Fixfj7NmzCA8Px5gxY9DQ0IAvvvgCoigiIyMDS5YscewBuZiS43nw4EGsXbsWJpMJCQkJGDx4MCorK3HhwgUEBgZi165dGD16tIOPyL3U19dj0aJFqK6uxhNPPNGt0OLU85JIDmU0GsXk5GRREASxsLDQ8npra6v41FNPiYIgiFlZWV3e3+OPPy4KgiD+7ne/s7zW3t4ubtiwQRQEQVy+fLmi9bsjJcf02LFjoiAIYmJiovjJJ5/YbNu3b58oCII4cuRI8dKlS4oegztR+nu0o4aGBnHSpEmiIAiiIAhiQUGBUmW7NaXHdPny5aIgCOKqVatEg8Fgef3jjz8WExISxPj4eH6PdnE8W1paxAcffFCMi4sTi4uLLa+3t7eLL774oigIgjhnzhzFj8GdnTp1SpwxY4blc9rdz7szz0sMLQ5WVFQkCoIgLl68+I5tjY2N4pgxY8SEhASxqanpG/cln2Bnzpwpmkwmm223bt0Sp0yZIgqCIJ45c0ap8t2SkmOanp4uCoIgbt682e72ZcuWiYIgiDt37uxt2W5LyfG8XWpqqnj//feLjz32WJ8KLUqOaUVFhSgIgjh9+nSbwCJ7/vnnxalTp4olJSVKlO6WlBzPo0ePdhpMWltbxfj4eFEQBLGhoUGJ0t1aU1OTmJ+fL44cOVIUBEGcNm1at0OLs89LXIjrYKWlpQCAGTNm3LEtNDQUEyZMgNFoxD/+8Y8u7ys5ORleXrZ/dVqtFtOmTQMAfPjhh70t260pOab+/v4QBAHf+c537G4fPnw4AOl6radScjw72rt3Lw4fPowVK1Zg5MiRitSqFkqO6cGDBwEATz75JPz8/O7Ynp2djdLSUsycObOXVbsvJcfT29sbANDY2Ihbt27ZbNPr9TCZTNBqtT2+HKomu3fvxuuvvw6dToft27dj7ty53d6Hs89LDC0OVlVVBQCIi4uzu/1b3/oWAOA///lPl/clCEKv96VmSo7pxo0bUVxcjAcffNDu9oqKCgDw6HVCSo6n7MyZM8jLy8PYsWORmpra+yJVRskxPXnyJABgzJgxaGlpwYEDB5CdnY3MzEy88847MBgMClXtvpQcz1GjRkGn06G+vh5r165FTU0NDAYDKioqsGLFCgDAkiVL4Ovrq1D17isqKgrp6ekoKSmxhIvucvZ5iXcPOdiVK1cAAAMHDrS7PTIy0uZ9ztqXmjlrHEpLS3H8+HFotVq7P+F5CqXHs62tDb/85S+h1Wrx8ssvW36y7UuUHNPz588DkGYB5syZg0uXLlm2vfXWW9i+fTtee+01xMbG9rJq96XkeAYEBGDLli1Ys2YNDh06hEOHDlm2+fv7Izs7GwsWLFCgavf3k5/8pNf7cPZ5iTMtDtbS0gJA+jDYI78uv68r+woICOj1vtRMyTHtTGVlJTIyMgAAKSkpGDJkSI/35e6UHs/8/HxUVVXh+eefR3R0tDJFqoySY3rjxg0AQFpaGoKCgvDmm2+ivLwcf/nLXzB58mTU1tZi2bJllvd5IqW/R2NiYvDoo4/C29sbCQkJSE5Oxj333AODwYBdu3bh3//+tzKF9wHOPi9xpsXBvL29YTabodFo7vo+sQt3nss/sSqxLzVTckztOXHiBJYvX46mpiZMnToVq1ev7tF+1ELJ8ZT73cyaNatH18c9hZJj2tbWBgDw9fXF7t27ERwcDAC477778Nprr2HevHmoqqrCW2+9hZSUlN4X74aUHM+6ujosXLgQer0eb7zxBr773e9afu8f//hHvPTSS/jZz36G4uJiDBo0SJH6PZmzz0ucaXGwwMBAAEBra6vd7fL16M5SqqP2pWaOHIe//e1vWLRoEfR6PaZPn46CgoI7Fpd5GqXGs76+HhkZGRg0aBCysrKULVJllPwelX9SnTt3riWwyHx8fPDYY48BAP75z3/2uF53p+R4/va3v0VtbS1Wr15tCSyAdNJdsmQJHnnkETQ3N2PXrl29L7wPcPZ5ybP/NXYD8vW8q1ev2t0uX+eT3+esfamZo8Zh69at+MUvfoHW1lY8/vjjKCgo6BOL8ZQaz23btqGxsREhISHIzs5GWlqa5ausrAwAcOjQIaSlpWH79u0KHoH7UfJ7NDw8HAA6vdQmv67X67tdp1ooOZ5Hjx4FAEyePNnu9ilTpgCwLoCmu3P2eYmhxcHk1e5nz561u11+vbNV8Y7al5opPQ5msxnr1q2zzKqsX78emZmZfWYBqVLjKV+zPn36NIqLi22+ampqAEh3GhQXF1tOHJ7KEZ/7zm67l08WnvwIDyXH89q1awCkWSp75M99e3t7t+vsi5x9XmJocbCHH34YAFBSUnLHNr1ej08//RRarRaTJk3q8r7ef/99mM1mm21Go9FyH/zUqVN7W7ZbU3JMAeC5557DgQMH0K9fP2zfvh2LFi1StF53p9R45ubmorKy0u6XPKYrV65EZWUl9uzZo/yBuBElv0fln/wPHjwIo9F4x/a///3vAIDx48f3omL3puR4jhgxAoC1v8jt5FnB+Pj4npbbpzgQ1XH2AAAFS0lEQVT7vMTQ4mAzZszA4MGDUVZWhr1791peNxgMWL9+PVpaWvDjH//YMgUMSH/R1dXVqK6utvlHauzYsRg1ahSqq6vx6quvWhY2mUwm5OTkoK6uDg899JDHf9iUHNOioiK8++678PHxwbZt2ywfwL5EyfEkiZJjOmvWLERHR+P8+fPIzs622VZYWIiSkhIEBwfjRz/6kXMOzgWUHM8nnngCALBlyxYcO3bM5s9555138O6770Kr1WLhwoUOPip1cZfzEh+Y6ASffvopli9fDoPBgISEBERHR+Pzzz/HlStXcP/992PPnj023Rdra2uRnJwMQOoi2PFa9pkzZ7Bw4UI0NTVh+PDhiI2NxenTp3HhwgUMGTIE+/bt6/R+eU+ixJiaTCYkJyejrq4OAwcOvOtPqklJSR59N4yS36P25OTkYPfu3X3qgYlKjunJkyeRkpICvV6PyMhIJCYm4quvvkJVVRX8/PywadOmHjcHUwslx3PDhg3Yv38/AKnZXFRUFM6ePYtz585Bq9UiJycHP/zhD517gG5g8+bN2LJli90HJrrLeYkzLU4wYcIEFBYW4nvf+x7++9//4siRIwgKCsIzzzxzxwftm8TGxuLPf/4z5s+fj+bmZhw+fBiA1OL77bff7hOBBVBmTCsrK1FXVwdAWi9w+zqMjl8nTpxw9CG5lJLfoyRRckxHjhyJ4uJiPPnkk/D19cWRI0eg1+sxe/ZsvP322x4fWABlxzM7Oxtbt25FUlISLl68iMOHD+PGjRuYM2cOCgsL+2Rg6Q1nnpc400JERESqwJkWIiIiUgWGFiIiIlIFhhYiIiJSBYYWIiIiUgWGFiIiIlIFhhYiIiJSBYYWIiIiUgWGFiIiIlIFhhYiIiJSBYYWIiIiUgWGFiIiIlIFhhYiIiJSBYYWIiIiUgWGFiLyKOXl5YiLi0NcXBwOHjxo9z0VFRV44IEHEBcXh/z8fCdXSEQ9xdBCRB5l3LhxmDZtGgCgoKAAJpPJZntNTQ1SU1PR0tKCefPm4Ve/+pUryiSiHmBoISKPk5aWBm9vb9TU1OC9996zvH758mWkpKRAr9dj6tSpeOGFF6DRaFxYKRF1B0MLEXmcESNGYN68eQCALVu2wGg04vr160hJScGlS5cwbtw4bNq0CT4+Pi6ulIi6QyOKoujqIoiIlHb58mXMnDkTBoMBGRkZ+OCDD3Ds2DEIgoC9e/diwIABri6RiLqJoYWIPNYrr7yC3//+95b/HzJkCPbt24eBAwe6sCoi6imGFiLyWFeuXMHDDz8Ms9mMkJAQ7N+/H/fee6+ryyKiHuKaFiLySO3t7diwYQPMZjMAoLW1Ff7+/i6uioh6g6GFiDyOKIp47rnncPjwYeh0OkRHR6OtrQ0FBQWuLo2IeoGhhYg8Tn5+Pg4cOIB+/fphx44dWLNmDQCgqKgIZ8+edXF1RNRTDC1E5FHeeOMN7Ny5E1qtFps3b8bo0aMxe/ZsxMXFwWQy4Te/+Y2rSySiHmJoISKPUVRUhJdffhkajQYvvfQSkpKSAAAajQbPPvssAKC0tBTl5eWuLJOIeoihhYg8wkcffYT169dDFEWsW7cOjzzyiM325ORkJCYmApBuhSYi9WFoISLV+/zzz/Hss8+ivb0dy5Ytw5IlS+y+T17bcvz4cXzwwQdOrJCIlMA+LURERKQKnGkhIiIiVWBoISIiIlVgaCEiIiJVYGghIiIiVWBoISIiIlVgaCEiIiJVYGghIiIiVWBoISIiIlVgaCEiIiJVYGghIiIiVWBoISIiIlVgaCEiIiJVYGghIiIiVfgfaeSEnxH65HMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "f_lower = m_star - 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "f_upper = m_star + 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "y_lower = m_star - 2.0 * np.sqrt(v_star)\n",
    "y_upper = m_star + 2.0 * np.sqrt(v_star)\n",
    "ax.fill_between(x_star.flatten(), y_lower.flatten(), y_upper.flatten(), color='red', alpha=0.25, label='$y^*$ 95% pred.')\n",
    "ax.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5, label='$f(\\mathbf{x}^*)$ 95% pred.')\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data')\n",
    "#plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also put the correct function there for comparison:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "f_lower = m_star - 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "f_upper = m_star + 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "y_lower = m_star - 2.0 * np.sqrt(v_star)\n",
    "y_upper = m_star + 2.0 * np.sqrt(v_star)\n",
    "ax.fill_between(x_star.flatten(), y_lower.flatten(), y_upper.flatten(), color='red', alpha=0.25, label='$y^*$ 95% pred.')\n",
    "ax.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5, label='$f(\\mathbf{x}^*)$ 95% pred.')\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "ax.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data');\n",
    "#plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You see that the true function is almost entirely within the blue bounds.\n",
    "It is ok that it is a little bit off, becuase these are 95% prediction intervals.\n",
    "About 5% of the function can be off."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's good.\n",
    "However, we have much more information encoded in the posterior GP.\n",
    "It is actually a probability measure over the space of functions.\n",
    "How do we sample functions?\n",
    "Well, you can't sample functions...\n",
    "They are infinite objects.\n",
    "But you can sample the *function values* on a bunch of test points.\n",
    "As a matter of fact, the joint probability density of the function values at any collection of set points is a multivariate Gaussian.\n",
    "We did it manually in the last lecture.\n",
    "In this lecture, we are going to use the capabilities of ``GPy``.\n",
    "Here it is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 1, 10)\n"
     ]
    }
   ],
   "source": [
    "# Here is how you take the samples\n",
    "f_post_samples = gpm.posterior_samples_f(x_star, 10) # Test points, how many samples you want\n",
    "# Here is the size of f_post_samples\n",
    "print(f_post_samples.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is ``test points x number of outputs (1 here) x number of samples``.\n",
    "Let's plot them along with the data and the truth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.plot(x_star, f_post_samples[:, 0, :], 'r', lw=0.5)\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data');\n",
    "ax.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, we see that the lengthscale we have assumed does not match the lengthscale of the true function perfectly.\n",
    "But that's how it is.\n",
    "In real problems, you won't know the true function anyway. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following interactive function regenerates the figures above allowing you to experiment with various choices of the hyperparameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0925290fa0db44e38f6059be33c27d13",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='kern_variance', max=1.0, min=0.01, step=0.01), Float…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact_manual\n",
    "\n",
    "def analyze_and_plot_gp_ex1(kern_variance=1.0, kern_lengthscale=0.1, like_variance=0.4):\n",
    "    \"\"\"\n",
    "    Performs GP regression with given kernel variance, lengthcale and likelihood variance.\n",
    "    \"\"\"\n",
    "    #k = GPy.kern.RBF(1)\n",
    "    k = GPy.kern.Matern32(1)\n",
    "    gp_model = GPy.models.GPRegression(X, Y, k)\n",
    "    # Set the parameters\n",
    "    gp_model.kern.variance = kern_variance\n",
    "    gp_model.kern.lengthscale = kern_lengthscale\n",
    "    gp_model.likelihood.variance = like_variance\n",
    "    # Print model for sanity check\n",
    "    print(gp_model)\n",
    "    # Pick test points\n",
    "    x_star = np.linspace(0, 1, 100)[:, None]\n",
    "    # Get posterior mean and variance\n",
    "    m_star, v_star = gp_model.predict(x_star)\n",
    "    # Plot 1: Mean and 95% predictive interval\n",
    "    fig1, ax1 = plt.subplots()\n",
    "    ax1.set_xlabel('$x$')\n",
    "    ax1.set_ylabel('$y$')\n",
    "    f_lower = m_star - 2.0 * np.sqrt(v_star - gp_model.likelihood.variance)\n",
    "    f_upper = m_star + 2.0 * np.sqrt(v_star - gp_model.likelihood.variance)\n",
    "    y_lower = m_star - 2.0 * np.sqrt(v_star)\n",
    "    y_upper = m_star + 2.0 * np.sqrt(v_star)\n",
    "    ax1.fill_between(x_star.flatten(), y_lower.flatten(), y_upper.flatten(), color='red', alpha=0.25, label='$y^*$ 95% pred.')\n",
    "    ax1.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5, label='$f(\\mathbf{x}^*)$ 95% pred.')\n",
    "    ax1.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "    ax1.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "    ax1.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data')\n",
    "    #plt.legend(loc='best');\n",
    "    \n",
    "    # Plot 2: Data plus posterior samples\n",
    "    fig2, ax2 = plt.subplots()\n",
    "    f_post_samples = gp_model.posterior_samples_f(x_star, 10)\n",
    "    ax2.plot(x_star, f_post_samples[:, 0, :], 'r', lw=0.5)\n",
    "    ax2.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data');\n",
    "    ax2.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "    ax2.set_xlabel('$x$')\n",
    "    ax2.set_ylabel('$y$')\n",
    "    #plt.legend(loc='best');\n",
    "    \n",
    "interact_manual(analyze_and_plot_gp_ex1,\n",
    "            kern_variance=(0.01, 1.0, 0.01),\n",
    "            kern_lengthscale=(0.01, 1.0, 0.01),\n",
    "            like_variance=(0.01, 1.0, 0.01));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "In the interactive tool above:\n",
    "\n",
    "+ Experiment with differnet lengthscales for the kernel. You need to click on ``Run Interact`` for the code to run.\n",
    "What happens to the posterior mean and the 95% predictive error bar as the lengthscale increases (decreases)?\n",
    "\n",
    "+ Experiment with difference likelihood variances. What happens for very big variances? What happens for very small variances?\n",
    "\n",
    "+ Experiment with different kernel variances. This the $s^2$ parameter of the squared exponential covariance function. It specifies our prior variance about the function values. What is its effect?\n",
    "\n",
    "+ Imagine that, as it would be the case in reality, you do not know the true function. How would you pick the correct values for the hyperparameters specifying the kernel?\n",
    "\n",
    "+ Try some other kernels. Edit the function ``analyze_and_plot_gp_ex1`` and change the line ``k = GPy.kern.RBF(1)`` to ``k = GPy.kern.Matern52(1)``. This is a kernel that is less regular than the RBF. What do you observe?\n",
    "Then try ``k = GPy.kern.Matern32(1)``. Then ``k = GPy.kern.Exponential(1)``. The last one is continuous but nowhere differentiable.\n",
    "How can you pick the right kernel?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Diagnostics: How do you know if the fit is good?\n",
    "\n",
    "To objective test the resulting model we need a *validation dataset* consisting of inputs:\n",
    "$$\n",
    "\\mathbf{x}^v_{1:n^v} = \\left(\\mathbf{x}^v_1,\\dots,\\mathbf{x}^v_{n^v}\\right),\n",
    "$$\n",
    "and corresponding, observed outputs:\n",
    "$$\n",
    "\\mathbf{y}^v_{1:n^v} = \\left(y^v_1,\\dots,y^v_{n^v}\\right).\n",
    "$$\n",
    "We will use this validation dataset to define some diagnostics.\n",
    "Let's do it directly through the 1D example above.\n",
    "First, we generate some validation data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_v = 100\n",
    "X_v = np.random.rand(n_v)[:, None]\n",
    "Y_v = f_true(X_v) + sigma * np.random.randn(n_v, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Point-predictions\n",
    "\n",
    "Point-predictions only use $m_n\\left(\\mathbf{x}^v_i\\right)$.\n",
    "Of course, when there is a lot of noise, they are not very useful.\n",
    "But let's look at what we get anyway.\n",
    "(In the questions section I will ask you to reduce the noise and repeat).\n",
    "\n",
    "The simplest thing we can do is to compare $y^v_i$ to $m_n\\left(\\mathbf{x}^v_i\\right)$.\n",
    "We start with the *mean square error*:\n",
    "$$\n",
    "\\operatorname{MSE} := \\frac{1}{n^v}\\sum_{i=1}^{n^v}\\left[y^v_i-m_n\\left(\\mathbf{x}^v_i\\right)\\right]^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE = 0.36\n"
     ]
    }
   ],
   "source": [
    "m_v, v_v = gpm.predict(X_v)\n",
    "mse = np.mean((Y_v - m_v) ** 2)\n",
    "print('MSE = {0:1.2f}'.format(mse))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not very intuitive though.\n",
    "An somewhat intuitive measure is [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination) also known as $R^2$, *R squared*.\n",
    "It is defined as:\n",
    "$$\n",
    "R^2 = 1 - \\frac{\\sum_{i=1}^{n^v}\\left[y_i^v - m_n(\\mathbf{x}_i^v)\\right]^2}{\\sum_{i=1}^{n^v}\\left[y_i^v-\\bar{y}^v\\right]^2},\n",
    "$$\n",
    "where $\\bar{y}^v$ is the mean of the observed data:\n",
    "$$\n",
    "\\bar{y}^v = \\frac{1}{n^v}\\sum_{i=1}^{n^v}y_i^v.\n",
    "$$\n",
    "The interpretation of $R^2$, and take this with a grain of salt, is that it gives the percentage of variance of the data explained by the model.\n",
    "A score of $R^2=1$, is a perfect fit.\n",
    "In our data we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 = 0.43\n"
     ]
    }
   ],
   "source": [
    "R2 = 1.0 - np.sum((Y_v - m_v) ** 2) / np.sum((Y_v - np.mean(Y_v)) ** 2)\n",
    "print('R2 = {0:1.2f}'.format(R2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, on point-predictions, we can simply plot the predictions vs the observations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IykqjRvrFRT5LU9Ly0UcfOSoOIiJyF/fuAZMni2XLSlPQXLmACRPEJof+/vrGRz5LU9LShZOuiIi8y5YtwIABwNmz5mP16okNDmvV0i8uImiciGtJUlISLl++jKSkJEe/NBEROcvt22I35latzAlLQADw8cdimIgJC7kBh2yzeenSJcyfPx9xcXG4efNm+vFChQqhWbNmGDZsGIKCghxxKSIicrQ1a0RX2ytXzMeaNQO++QaoUkW/uIiy0FxpiY+PR5cuXbBy5UokJiZCluX0P0lJSVi7di0iIiKwc+dOR8RLRESOcvUqEBkJhIebE5aCBcV+QXFxTFjI7WiqtFy/fh3Dhw/HnTt3EBISgt69eyM0NBQFChRAUlISjhw5gh9//BH//PMP3nrrLaxduxZPPfWUo2InIiJ7yDLw/ffAqFFAhuo42rUTCUu5cvrFRpQNTUnLokWLkJSUhBYtWuCLL754oj9LzZo10a1bN4wYMQLbtm3DsmXLMGLECE0BExGRBgkJov3+xo3mY8WKAbNnAy+/zP2CyK1pGh767bffkCtXLkRFRVltKJc7d25ERUXBYDBg8+bNWi5HRET2MpmAr74SGxxmTFh69gSOHwdeeYUJC7k9TZWWy5cvIyQkBIGBgdmeV6xYMYSEhOD8+fNaLkdERPb4+2+xMmjHDvOxMmWAefOATp2cdtmEBLGCOjlZTJVp2RLgmgzSQlPSIkkSHj16pOrcR48ewWQyabmcJsOHD8fw4cN1uz4RkcspGxz+97+iHb9iwADgk0+AwoWdctn4eOCDD4D168X0GT8/UeiRJKBDB9G3LizMKZcmL6cpaQkODsbJkydx6dIlPP3001bPu3jxIk6fPo2QkBAtlyMi8jl2VysOHhQt+PfvNx+rWFEsY27RwmnxxsSIBUmybG6mq3xelWVgwwYxOvXTT0BEhNPCIC+laU5Ly5YtYTQa8fbbbyM5OdniOcnJyRg7dixkWUbLli21XI6IyGfExwMdO4qNlPv2BUaPFl+Dg8WIzt69Vp6Ymipa7devb05Y/PyAt94CDh92asISHy8SFqNR/LFEeSwyMpvvgcgKTZWW1157DT/99BMOHDiAtm3bokuXLggNDUXBggWRnJyMo0eP4ueff8aNGzdQokQJ9OnTx1FxExF5LburFTt3iurKiRPmY6GhwMKFQMOGma7hjPkmUVGZY7ZGOScqSvS1I1JLU9JSqFAhREdHo3///rh+/Tqio6OfOEeWZZQsWRLz589HoUKFtFyOiMjrZaxWWLv5G41ifkhkpMhTwqrfBd59F5gzx/yk3LlFxWXCBCBPnkyv74z5JgkJwLp1OScsGb+HtWvF8zg5l9TS3Ma/atWq+L//+z/88MMP2Lp1K86cOYN79+4hf/78qFChAlq0aIGXX34ZBQsWdES8RERezeZqxYhrWHOlAZBxdWaDBqK68p//ZHqOM+ebbNmiPmHJ+D3ExQGvv27b88h3OWTvofz582PgwIEYOHCgI16OiMgn2VWt2F0cCTAhCADy5hVZz8iRgMGQ6Vy7Kjg2VFySk81VG7X8/IA7d9SfT+TwXZ6JiMg+dlUr4Ic4tABeeAH46y8x4TZLwgLYN9/EFgUL2pawAOJ8zhogW6iutKxcuRIA0KZNGxQoUCDTMVt069bN5ucQEfkCu6oVMOJO5EBgWSOrHW1dMd+kZUtxeVuSLkly6mIm8kKqk5ZJkyZBkiTUq1cvPWlRjtmCSQsRkWV2VStgQKE2zwHZ/FPsivkmQUFiIu+GDdaXO2dkMADt23MSLtlGddJSpkwZ8YRcuZ44RkRE2jmrWuGq+SaTJ4uJvDl9D5Ik/kyaZNvrOwO3GvAsqpOWuLg4VceIiMg+zqpWOGq+SU43+LAwsfJIWaFk6XswGETCsny5vq38udWAZ3LZRNykpCQcO3bMVZcjItIsIQFYvBiYPVt8TUhw/jUnTwYkSYaE7LMMW6oVSgXHFhkrOLZ0542IECuP2rUzX9PPz/ya7duLx7t0sS0eR4qJARo3FlUha0u/n3tOnEfuRdOS5+rVq6NevXr4/vvvczy3b9++uHr1KnZk3GWUiMhNZKwiXL8O7Nol5nS49FP4o0couWIBBpn8MA+DABgh48mVQLZWK7RUcOzp7RIWBsTGivc0Lk4MMxUqJJIgvYdenL30m5xLU9IiyzJkFYOvKSkpuHbtGu5wQT4RuZmswwSW5mOoacCmdW5E/NIT+GD4Vay/MxQy/OCXnrDIAKT0uJRqxaRJtt1M7ZlvovUGHxRkf+M4Z8014VYDnk110nLq1CkMGDDgiSTlr7/+QvPmza0+T5Zl3LlzB6mpqQgODrY3TiIih0pIAD7+GJg3T/xd+actp5uZUqno0UNUY2RZ49yI+/cR8+oqRP4cCRmVIT8etTelV1ik9OGVoUOBcePsu3nbM9+kUyfX3+CdOdeEWw14PtVzWipXroy6devi33//Tf8DAA8fPsx0LOufq1ev4v79+5AkCUOGDHHaN0JEpIYyP6N8eWDuXHFDtHWSKiBuaK1bi7kPds+N2LED8VV7I/LnSBhhgNHK50iTSbzeggXA1au2x6qwZb6JcoNXM5wEZL7B28vZc020LP0m92DT8NA777yDJk2aABAVlHfffRfBwcEYNGiQ1edIkoT8+fOjatWqCGKqSkQ6yjg/wxGSkrJ/3OrQSXKy2Mhw7lxEYQ1kSOkVFmscVc1QO9/E1XsJ2TMUVbKkbUNI3GrA89mUtDz11FPokmHK97vvvotixYplOkZEZIne/TDU3BSd4Ylk4//+Dxg0CEhIQALKYR065JiwKHIarrDlPc5pvomrb/C2zDUxmUS17No124aQnLXVgN6/275E00TcEydOOCoOIvJS7tIPQ+1N0RlEsiEjoetbCIr5PP34ljztID+0rfOEpWqGM95jV+4lZOtcE5Mp8zCZ2p2qHd28z11+t32JSzdMPHDggCsvR0Q6c5d+GLbOz3AGWZYQF3PLfKBlSySPj0qfU6JW1mqGs95jrb1dbGHPUJQ1RqP4ExmZuX8MYF76bWE/SYsMBlHRsVQ1cZffbV+jqdICAFevXsXSpUtx8uRJpKamwpQlNTcajbh//z6uXbvGBnNEPsSd+mE48qZoLz8YcQeFgMKFgc8+A954AwW/lTRVM5z5HrtyLyF7hqKyk938H3u3Gsjax2f6dPf43XYldxgG05S0XLt2DV27dkViYmL6UmhJkjIti1Y2VJRlGf7+/louR0QexJ36YTj6pmgPEwwo9ExlYN0x4PG+bVqHK5z9HrtqLyF7hqJyYm3+j61Lv2VZVFuyDgGp4S29XtxpGEzT8NDixYtx48YNBAQEoGvXrujduzdkWUb9+vUxaNAghIeHo9DjjwSNGzfGnj17HBI0Ebk3PZbLZscZN0VbSZKMFj8PT09YAG3DFa54j8PCgDlzxM3J2jCWwSD+aNlLyJ6hKDWsLVdWu/Rblq0PAanl7N9tZ3O3YTBNScuOHTsgSRLmzJmDDz/8EBMnTkThwoVhMBgwevRoTJ8+HevXr0flypWxa9cuHD9+3FFxE5Ebc7d+GM66KaplMMjo2FFCUPkngxB7DeUcX9ZqhrPfY6WfzZAh1nvZOGovIVuTN7WyW82kLP0+d07sKzVrlvh67pyoisiyeehN61woT+31knH40dp7kN0cImfQlLRcvnwZxYsXR+PGjdOPVa9eHYcPH04fIipevDg++OADmEwmVXsUEZHnU4ZjbOHMfhjOuimqIZINyerQiTJcoVQsLLFUzXDme2zp03VGSuVl3jxxg3fE0IDa5M0WalYzKUu/R4wQX5WhJEeuNvPUXi/2DD86m6ak5cGDByhVqlSmYxUrVkRqaioSMtTC6tSpg5IlS+LgwYNaLkdEGeixA7Farlwuq5YzboqC/PjPk9QOndizM7Kz3mM1n66Vm9SwYY77dK0mebOVvauZHL3azNm/287gbkO8Ck1JS+HChZ/YBLFs2bIAgNOnT2c6/tRTT+HGjRtaLkdEMJftg4OBvn2B0aPF1+BgsVeMK0q0OXHlclm1nHFTNCANBhhRH3shQWQQfpKyKMG2oZOchiuyJj3Oeo/1/HSdU/JWsqT66lJ2y5Vz4ujVZs7+3XYGdxviVWhaPVS1alXs3r0bFy5cQLly5QAAwcHBkGUZR48eRYsMP6WrV68iT5482qIl8nEZ29BbmxRnrbGWK7lyuawtlJviBx/Y1szMEgkmtMd6TEIUwgwHkDAwCnF13sKd1DwW2+KrpXZnZGe8x+6woWB22wxcvSomfeaUVGldzeTI1Wau+t12NHfd8kBT0tKyZUvs3LkTAwYMwIQJE9CsWTPUqVMHuXLlwg8//IDw8HCUK1cOS5cuxfXr11GjRg1HxU3ktaz1QtC774mtPRpctVzWFgkJwJEjQKtWwPPPA7dvA9Om2bjkGDI+wRh0x0oE4QJQuzawcA+C6tXD606LXMj6MxgwwLHvsav3G8qOpeQtKMj2nart4ajVZq783XY0dxziBTQmLd26dcP//vc//PPPPxg6dCgOHDiAwMBAtGnTBuvWrUPbtm2RP39+3LlzB5IkoX379o6Km8jr5NQL4fZt9WV7oxEYOFAMK2j9hJc1LuUGmVOPBjX9MJRSf58+IpkoWdL2eNUkU9m9tyVKADduqKxWIA3tsR5jMAvIkweYEgWMGwfkzm1b0DbKLv569QCl2bjWm7i7frrOyFK1LOP70b69SBK0JOz29M/JyhHJk54cveWBo2hKWvz9/bFkyRJ8/PHH+PPPP9OHf9555x0cO3YMZ86cQdLjbVDr1q2L3r17a4+YyMNZusnu25f9sM/69bbdSGQZOHhQzHPJmljYUjGJiQF69BDXVuLK+HXdOjE8sXz5k8NRCQliF+SRI4HNm4FDh8TxjDdF5evixcDCheIfvZYtgUaNgOLFs49PbcOrnIbUrl9X995KMEGCjEmIEmMU0dFA9eo5PzHLe2JrR9Gc4t+/X3zPzzwD/Pmntpu4u366zkrtTtX2snXoTeHo5ElP7jrEK8myllzSzGg0wpBhdtvDhw+xefNmXLx4ERUrVkSLFi3gZ+v6PA8RERGBo0ePIjQ0FDHcaIKsyO4m68wW88onvqgoYMcO6zf5AQNExUG5oRYrJhIRtf9g7dol/oHO7vusXRsoV078Qwhk/9rZVXQy3sgtvYZSlh83Dpg5U/3OzgaDlYoQjABkzMszCgNnVgXefNOm9cbZvSc1aoj3uX//J//Bj40Vk3jVJBIGA/Dzz0Biov038YQEkeja+un63DnPm7ORk717RW6a0++Osvx74kTx34wjkye92fIeGAz2D0nbdA+VNUhISNDydK/RpUsXOSQkRO7SpYveoZCbWrVKlnPlkmWDQfm8rM8fPz/HnGPpz/PPO+/7NBjE665aJct79oj/L0mOf29KlpRlSTI9PmbK8Lj4/5Jkkjt2lOX4eFk+f16WFy2S5S++EF/Pn9f+s1dee88eWe7QwfbvoX597b+rHTuq//kZDLLcqZNtr6/2fXMHOf3slN/LmBi9I3UeV7wHttxDYf9lZLlatWpyr1695JiYGDklJUXLS3k0Ji2UHWfdZN3xj8HgvO9TksT72LSp85I/STLJ06p+K/vhkSzBaPEcP7/M36OS5EmSOemQZXEznjTJtiTQz0/8MRjs/x5jY7X9vsbHq/t9VX4eyver5r+DDh3Mr2vtfXM38fEiPktxd+rkvnE7krPfA1vuoZqGh6pXrw5ZliFJEvLmzYs2bdqgS5cuCPPUQTw7cXiIstOpk+1j457KFUNdzn8fTQCkx39so4yQ16kj5po4872wpk4d88Rce+U0/JZxkqmaHjRqX0/vpfrZcdb8GU/irPfAlnuopqTl33//RWxsLGJjY3Hq1CnxgpKEsmXLokuXLggPD0eZDJuDeSsmLWSNPXMESE/KD0rHjYo0ctQck717ra/Q6dhR/STT+HixJYCz50WQ57LlHqppZmypUqUwcOBArFu3DjExMejduzcCAwNx4cIFfPnll2jVqhX69u2LtWvX4sGDB1ouReSRHN1Zk5zNvgqLO5Flx3QltbVDrzXuuH8NeS5NS54zqlGjBmrUqIF33nkHO3bswJo1a7cxcbYAACAASURBVLB161bs3LkTu3btwvvvv4927dph6tSpjrokkVtLSAB+/dX5QyZEGSl9U+xZXm2J2g69lrhDh13yLg5fg2wwGNCsWTN89tln2LlzJyZMmIB8+fLh7t27WLFihaMvR+R2Mu4NtGwZExZyLZMJWLTIPfamctf9a8hzOazSktGNGzewfv16bNq0CQcPHoTpcZOBqlWrOuNyRG7DUiMwcjxH7QvjrZRGfoC+e1N5Qodd8iwOS1pSUlLwyy+/YO3atdi9ezdMJhNkWUbhwoXRsWNHREREcO8h8mpq9gYibQwGMalz507HJS2+lAA5c28qSzylwy55Dk1Ji9FoxPbt27F27VrExcUhNTUVsizDz88PTZo0QUREBFq2bMndncknqJ1wSPZRutzOnAlcuCBuvGlpNjwfJsiPJ9r6STJMsgRJAmrVElse+IqME17XrHHutdx1/xryXJqSlqZNm+LWrVtQVk2XL18eXbt2RefOnVGyZEmHBEjkCWydcEi2ybr5XFiYqBSMGQNs357z8yWYYIARMX3WILFpF9y5Z0jvMwH43rJ0eye82jq5NyhIvMdxcereX1ftX0OeS1PScvPmTeTLlw9t27ZFREQE6tWr56i4iDyKlqXNXF0k3oOGDcUGi8ePi2M5bT4XFgb8/jvwzjvAjBnWX9sPafCTgOWzr6HjsG4Wz7FnczxPp0x4VbMySO3mlJaeozZhUSppkybZ9e2Qj9CUtHz00Udo3LgxSpQo4ah4iDySPRMOJQl4+WWgShXxj7u3zauYORM4exaYN0/8PbvvT5bFTS7jxootWgA1a2bfdTMmBvj00+w65cqQYcCH02R0Gfa01etPniwmqKpNIF09D8YZia3aCa857TJtaXKvrRPSs1bSiKzRtOR5/vz5aNu2LW7duuWoeIg8kj0TDmUZaN0aKF/eeTdAyY4+aZIEdO6s/brduwNz5gC7d4tKiRJLxs2RM8aX8UZ4+DAwe7aYkGktYTFPfJazqZCIj+8TJ/tlu9Q3LEzcdA0G65s3Kx1bZ8yw/P1Iknid7F7DHpIkWuUvXgz897+Oe201E14zTi639h4rj0VGiuXUap6TVfv2YrhPzZYA5Ns0VVquXLmC4OBgFC1a1FHxEHkkrRMOnTVEZM/ryjIQHi5uavYMmWSdl6B0VlX2LfnrL+CLL8TrW4vNZBJ/unUTN+s+fZ48R0x8liHL2Wdmaieeli0LPPsssGOH5cebNBFVnbAwYNw46/uw7N0LvPEGcPRotmGpJsui78/rr4v3wlEJrpoJr/Z0s824rWJO/PzEfzvOnhBM3kNT0hIYGIjk5OT0TROJfFVQkG3zIrLe2B09p0Ipt8+dCwwebF8yFRpq25CJ8lxr8xKUzqqdOom/q3lNWRbPKVgwc1+RhHMmrFsn5ZiwKLJOPM06ofThQ2DYMOsxGQzArl1i1ZIyfGGtU2xYmJgg3LevqtBylDG5sCc5tkTNhFd7utnGxtoWn8kEbN7MDriknqZC45AhQ3DlyhVMmzYNqampjorJYc6ePYuxY8fihRdeQK1atfDiiy9i1qxZSElJ0Ts08kKTJ5tv2tmxdGNX+9ycXlf5qpTbBw4UCZGy+3BODAbxqT4oKPOQiZrnK+dlNy9BuRHampz16JGhk+s//2BLm49VJywKWQaio83dijN2ix08WCyfVjsEkhMluXCEJk3MN3QlOVb787RE7YRXeyeXswMuOZPm5nJ169bF999/jxUrVqB69ep46qmnEBAQYPFcSZIwI7tp/g50+PBh9OnTBykpKahVqxZq1qyJ/fv3Y/78+di6dSt+/PFHFChQwCWxkG9QbvLKBERLN0BrEw7VPNcSZZ7FhAlA8eKWt4tXO8nU0s0sIkIkPxl3+7X2XEsrfLKy90ZoNAJj3zLht06fAlOmIDl1APxghAnq796SBHz4Yeb3wZahFlv6m9haectO1uTH1knDGdky4dXeyeWAbXGxAy7ZQlPS8t5770GSJMiyjNTUVBw4cMDieco5rkpa0tLS8NZbbyElJQUffvghunUTyxxTU1MxevRoxMXF4bPPPsOUKVOcHgv5Fks3+ZyW7mb33OxkvAFlN4FRSzKlPD/jnJQ7d4BHj8RjuXNbTpSssedGqPh9h4QFO/7BIKSiIJJtSlgAxzT+s6W/iZbkIqPt2zNfT83PM+M11f7+ZWXv5HJbsQMu2UJT0hIeHu6Wc1nWr1+PCxcuoFGjRukJCwAEBARg2rRpaNGiBZYvX46RI0eicOHCOkZK3sjSTV7tjd3SpNW4OLGXjC0JUFZakimFlt1+FfbcCM0kDMVXqIuDaPlGeUjf5jwJ1xlkWVS2WrXKvrmavdUzS9fL2k8lp59nx45A//5AYqJtv38Z2Tt/hh1wyZk0JS3Tp093VBwOFfd4gLR169ZPPFa0aFE0bNgQW7duxfbt29GhQwdXh0c+QstNPutz7UmAstKSTDmK1omkMiRENf0/rFkUiMb/WF/p42zLlgE//ph9czXA9uqZJdaGT5z987R3crnSu8WeCelEOXHKLs96O3nyJADru0pXrlwZW7duxYkTJ5i0kEdwRJXDGa9lq3//1TZUIsOAtTsCsWCBWM2jF+V7ULNzcsbk4v33gUWLbLtWTsMnzvx52jsfyt45VEQ5cVgLpNOnT2PhwoWYOHEiRowYAUDs/Pzzzz/jkTIA7iLXrl0DAKv7HykdfJXziMg1oqK0N0eTZeDNN9UPM2ldlZUTtSuLgoKA996zPRY9h0/UrCDLumrMnucQqaU5abl//z7Gjx+Pjh07YubMmVi1ahV+/fVXAMDFixcxYcIEtG3bFgkJCZqDVUtZ0mxtFZNynEufiVxHWe7siOZotkyqdcXO2xlXFmXH1iXLGZeg60UZ4mrXznIXYEvdbO15DpEamoaHTCYThg4dit27d8PPzw/Vq1fH5cuXcfv2bQDAgwcPkCtXLly8eBGvvvoq1qxZg8DAQIcEnh2DwQCTyZTjJGHZ2f+SEVE6LZtKZuWO+zSpXVmkZQm6XuyZP+MOc6jI+2iqtKxatQq7du1C+fLlsXr1aqxatQoVKlRIf7xmzZrYuHEjKlSogBs3buDbb7/VGq8q+fPnByCqQJYojfDy5s3rkniIfEFCgmgzP3u2+Jq1uKosd/ZmahqlqRk+8fMTCcugQYCVUW5dKPNnRowQX9UkH/Y8h8gaTf+ErF69GpIk4fPPP0eVKlUsnlOuXDl88cUXAICtW7dquZxqypyV69evW3xcmcvC3amJtIuPt9xlNjhYtOxX5nloW+4suLLDgj3XUtsozdLwSdbNI2VZbMOQ9X0k8mWakpaTJ08iKCgI1apVy/a8kJAQlC9fHhcuXNByOdWUVUOnTp2y+Lhy3NrqIiJSJyYGaNxYDHdk7TKrrKx57jlxnljubP/4kLMn1BoMQK5cwIIFolLUs6ftr2FLozRl+OTcOTGxOOv3l3WFkvI+EvkyTUnLgwcPkC9fPlXn5s+f32VzSJo1awYA2LRp0xOP3bp1C3v27EHu3LnRuHFjl8RD5I3i48WKGWX1jCXmlTUyrs5ZgQ5+G2BAms3XUoZS5s1zTOKS3eTQgQPFMMb06a5Z6fPvvyJRym7CsK17HxF5K01JS6lSpXDu3Dk8fPgw2/NSUlJw+vRpq0uQHa1169YoU6YMduzYgR9++CH9eGpqKiZOnIiUlBR069YNxYsXd0k8RN4oKkrdyhxZBuQ0I6I+yYPJxv9CggwJ6seJtGwAaYmfHzBliqimzJolvp47J/YTyrj81lUrfWx6H1WsUCLyZpqSlueeew6pqalYsGBBtufNnj0bDx48QKNGjbRcTrWAgABMnz4dAQEBmDp1KiIiIjBixAi0bt0aW7ZsQY0aNTB27FiXxELkjWzdrdmIXFiLjiiJq/ipVTQMuaQce3j07Ws5odC6I7bJJOaJqJkcqmXnbjVsfh8zrFAi8kWakpZ+/frB398f8+bNw0cffYQjR46kV11SU1Nx+PBhvP3221iyZAly5cqFPn36OCRoNRo2bIgVK1bgpZdewuXLl7Ft2zYULFgQQ4cOxXfffccdnok0sGf5sgw/xI3bhIhfh2DnTinbHh67dgELF1pOKNSsvsmOLUM4zm6UZtf7qGKFEpG30tSnpVy5cvjkk08wZswYLF26FEuXLk1/7JlnngEgeqEYDAZMnToVFStW1BatjUJCQjB79myXXpPIF9izW7Ofn4w7T1cHoL2HR8Y9fdauVR+DPXvdOGKzSWvsex/VrVAi8kaa9x5q3bo1li9fji+//BLbt2/PNL/FYDCgQYMGGD58OOrWrav1UkTkJuxZvmwySci6o4eWfXOUxGftWiA8POd4tDRrc1ajNPveR/UrlIi8jUM2TKxWrRrmzp2Lhw8f4vz580hOTka+fPlQrly59EZvROQ97N2t+e23gd9+s74rsj06dgRWrBAra2TZ8vwQg0HEq3WvG0dvTmjP+6jnXkREenNof8o8efKgSpUqqFu3LqpVq8aEhchLpa+s8bOtTOCsniOeuteNJ+5FRKQnh1Rarl69ijt37mTqivvtt98iNjYWRqMRzZs3x6BBg1T3dCEiN3fzJibLc7DRNAESxCRbtYxGkUhERopEwlEVF0/d68YT9yIi0ovmSsvs2bPRsmVLLFq0KP3Y/PnzMWPGDBw7dgx///03vv76a/Tt2xdGtev6iMh9rVoF1KiBsHXv4SdEwgCjzQ3jnNlzxNP2unH2CiUib6Ipadm2bRu++uorpKWlpW9C+PDhQ0RHRwMAXnjhBYwfPx6lSpXCoUOHsHz5cu0RE5E+rlwBunYFunUDrl4FAEQU2oKd765Hu462rz1mzxEzTx3eInI1TcNDK1euhCRJGD16NAYOHAgA2LVrF+7evYvixYtjzpw5MBgMaNKkCTp16oQNGzbg5ZdfdkjgRNYkJIj+F8nJYnVGy5bu/2nbrckysGSJ2Anx9m3z8U6dgK++QtjTTyMWwMyZYqKtrS8dF+fYya2eylOHt4hcSVPScujQIQQGBmLAgAHpx7Zv3w5A7P9jeFzrrFKlCoKCgnDy5EktlyPKVny86KWxfv2TvTQ6dHDsihWfce6c6J3/66/mY089BXz5JdCjR6ZWsXnysOeIIzh6hRKRN9GUtNy+fRvVqlWDlOEfrp07d0KSJDRs2DDTuQUKFMClS5e0XI7IqpgY85JXa7sNb9wo5g5EROgXZ1ZuWxUyGoGvvgImTADu3TMf79VLbNhjYd8uX+o54rY/NyIvpylpKVKkCO5k+Jj077//4syZMxaTlitXrqBgwYJaLkdkUXy8+NCf3TxvZ61YsZdbV4WOHwf69xdvlKJsWbEVcbt2Vp/mCz1H3PrnRuQDNE3EDQ4ORkJCAk6dOgUAiI2NBSDa52fc0XnNmjW4efMmqlatquVyRBa9+aa6DefcZZfcmBigcWNR+bFWFcquj0lCgthIcPZs8dVhE1kfPQI+/BCoUydzwjJkCHD0aLYJC+D9PUe0/tyISDtNlZa2bdti79696NOnD5555hls27YNkiShy+Mp7v/++y+io6Pxv//9D5IkITw83CFBEyliY4F9+9Sfn3HFih43y/h4Ue0xGq1XJKxVhZz6KX//frGt8qFD5mNVqgDR0cDzz6t+GW/tOaLl50ZEjqOp0tKzZ0+8+OKLSExMxObNm5GWloawsDD06tULgGg69/333yMtLQ3du3dn0kION2WK7c+xZ5dcR1U3oqIyz7vJLsaMVSGnfcq/fx945x2gQQNzwuLnB4wbJ/5uQ8ICeG/PEXt/bkTkWJoqLX5+fpg9eza2b9+OEydOIDg4GC1atEhfNVShQgW0atUKnTt3RuvWrR0SMJEiISFzYUAtW1asOLK6kZBg3iVYDaUqFBvrpE/527eLuSsZV/XVrAksWgTUr68uSAucuSuyHuz9uelVzSPyZg5p49+0aVM0bdr0ieOFChXCnDlzHHEJoids2WLf89SuWHH0iqQtW2zfYFCWgffeU/8p32QSn/LXrMnmxORkUV356ivzsTx5RCYxfrz4/xq5U88RrSt97P25sf8MkeM5JGlRnDt3DqdPn0ZqaioKFSr0xIRcIkdKTrZvp2E1K1acMYchOdn2PiaSJKpJar9Hk8mcLFi8MW/cCAwaBFy4YD727LPAwoVAjRrqA1NJz54jjqqS2fNzY/8ZIudwSNISExODBQsWIMHCQH+NGjUwatQoi5UYIi0KFrQ9YQGA2rVz/qRtyxwGoxF4993M/dcssaePiT3fHyDmz06dmuFAYqLoaPvdd+Zj+fIB06YBw4apX/LjIRxZJfOl/jNE7k7zhokTJ07ExIkTcf78eciyjAIFCqBkyZLIly8fZFnG0aNHMXDgQCxevNgR8RKlU/qC2CrTzdwCZQ6D2v09ZRnYvBlo3RrYu9f6efbG62fHf6U//5whuOXLgerVMycsrVoBR44AI0d6XcKSsUpm7WeoPBYZmf3PDLDv5+Zp/WeIPIWmpGXjxo1YtWoVDAYDhgwZgq1bt2Lv3r3Ytm0b/vzzT/zyyy/pK4k++eQT7N+/3yFBEwG29wUBgMKFgVKlsj/HnjkMgJjDkN0KHnv6mNSpY/unfEC0VUnYe1WUESIjgevXxQNFioiJtr/8AlSoYPsLewBHr/Tx9v4zRJ5EU9Ki9F+ZOnUqRo4cidKlS2d6PCgoCJMmTcL48eNhMpnwzTffaAqWKKvJk809P9S4ezfnpcHKHAZbmUw5f3pXG69yTk5VIWtkGYhr9j6werX5YJcuwLFjwBtv2Ffy8QC2VsnU7jRt68/NU/rPEHkaTUnLsWPHULJkSUTkMCjcp08fFC9enJUWcriMfUHUJBpqhgXsmcOgyOnTu619TDp2BEJDbY/DD0bcuf94ylqJEuLFVq0Csnyw8DZaVvpkx1v7zxB5Gk1JS1paGopb2DgtK0mSUKpUKTx8+FDL5YgsUvqCPPWUuvNzSizsnXuiyOnTuxJvu3bm6ygJl9LHZOdOURhRzreVCQYUwh3gtddEdaV7d6+trmRkT5VM7UofW39uROR4mlYPhYaG4siRI0hKSkLhwoWtnnf//n2cPXsWlStX1nI5IqtKlgSuXVN/fnYNwJQ5DBs2qB9myCqnPh229DHp3988T0MtCSa0WPI68Fpz+74BD+XslT7u1H+GyBdpSloGDx6M/v3745133sEXX3yBPBaaUsmyjKlTp+LevXvo16+flsv5DG57bztHNwBTu4eONWo/vavpY2JrEmWQjGjf1oQgH0tYANftNK1n/xkiX6Y6aVm5cqXF4/Xr18e2bdvQsWNHdO3aFaGhocifPz9SUlJw5swZrF69GkePHkWbNm1QpkwZhwXujbjtvf0c3QBMmcOQU4M5axzdp0P9RoQyJIMBk/7rXcuY1bI5wTOIYR1+KCDyDKqTlkmTJkHKZkz8/PnzmDVrltXHN23ahF9++QXHjh2zLUIf4eiW8b7GGcMCyhyGCRNs3zLA0X06zEmUDNloglF+MikxGGRIkuTzE0G9dadpIrIhaWGVxHm47b12zhoWCAszN46Li1OXGDnr03tEsd+ws9QX+ODi61iHDpDhBz+YYILf44mgkkdtROgsGatkSsfirAwG8fP39QSPyNOoTlricloTSHazpxlWthvi+SBnDwtMmyb6u+T0c3LKp/c7d8RGhvPnIwxALH5GQp7KiOs4C3cat0WhopwImpW37TRNRILmvYdu3ryJkydP4ubNmwCAokWLomrVqggMDNQcnC/gtveO48xhAd0+va9fDwweDFy8aD723HMIWrgQr1er5qCLeCeu9CHyPnYnLbGxsfj+++9x5MgRyBbuEKGhoejVqxfCw8M1BejtuO294zg7sXDpp/cbN4BRo4AffjAfy58fmD4dGDrUvpa9PoorfYi8h81JS2JiIt599138/vvvFpMVxZEjRzBhwgSsW7cOM2bMQLFixTQF6q247b1jOTuxcPqnd1kWmdfw4SJxUbz0ErBgAVC+vAMuQkTkmWxKWu7du4fXXnsNZ86cgSzLqFOnDl588UVUr14dxYsXh8FgwK1bt3D8+HFs3rwZu3fvxh9//IFXXnkFMTExyJ8/v7O+D4/Fbe8dzxXDAk759H7pEjBkiBj/UxQtCsyaJTrb+kBHWyKi7NiUtLz77rs4ffo0SpQogalTp6J58+YWz6tXrx569eqFvXv34u2330ZCQgKmTJmCTz/91BExexVXNcPyRR4zLCDLQHQ0MHZs5hJat27Al1/mvC01EZGPUD0wfuDAAWzatAmFChXC4sWLrSYsGYWFhWHp0qUoUqQINmzYgMOHD2uJ1Stx23sfd+qUyFwHDjQnLCVLis0NV6zQLWFJSAAWLwZmzxZfc9oFmYjIFVQnLT///DMkScLQoUNRqVIl1RcICgrCqFGjIMsyVq9ebVeQ3o7b3pv5zM3SaAQ+/RSoVQvYutV8/I03gOPHdesgGB8vkuLgYKBvX2D0aPE1OBjo1Mn6zthERK6gOmn5888/kStXLvTo0cPmi3Tq1Al58uTBXv6LZxG3vfexm+WRI0CjRmI46P59cSw4GAnf/YbFTRdh9ndFdUnYYmKAxo3FsnFrXZmfe06cR0SkB9VJy+XLl1GmTBnky5fP5ovkzZsX5cuXx8WMvSYoE1/e9t5nbpYPHwL//S9Qt645C5MkxPeYiY7V/kHwa8/rlrBl7MpsrTmf8lhkpJclkUTkMVRPxDWZTChYsKDdF/L390daWprdz/cFvtgMy2e2MNizB+jXDzh61HysWjXE9P4Zke9V033PKXZlJiJPoDppCQwMxOXLl+2+0JUrV1C0aFG7n+9LPGbViwN4/c3y3j0xaenzz83fZK5cwPjxiH9pMiJb+OuesLErMxF5CtXDQ9WqVcOtW7ewf/9+my9y8OBBJCYmokaNGjY/l7yXcrNUs1cQkPlm6RHi4sRE21mzzBmBMjQUFYWoT/xtTticQUtXZiIiV1KdtLzwwguQZRmzZs2y6QImkwmffvopJElC69atbQ6QvJdeN0unr1C6fRsYMEAsZT5zRhzz9xct+PfsAerUcauETenKbAt2ZSYiPaj+pyo8PBylSpXCvn37MHXq1Gxb+CvS0tIwadIk7N27F6VLl0anTp00BUvexdU3S5esUIqNBUJDRbM4RdOmwOHDYqfmXGJE1p2qG+zKTESeQvUtI0+ePIiKioKfnx+WLVuGnj174pdffsG9e/eeOPfBgwfYtGkTunfvjp9//hn+/v74/PPPkTt3bocGT57NlTdLp69QunYN6NkT6NwZUOZ+FSgAzJ0LbNsGhIRkOt2dqhtKV2ZbsCszEenBpjb+TZo0wYcffogpU6bg0KFDGDlyJCRJQtmyZVGkSBHkzp0bSUlJOH/+PNLS0iDLMvLmzYtp06ahVq1azvoeyEO5agsDp65QkmXgxx+BkSOBxETz8TZtxAaHVmaqulN1Q+nKvGGDuuEqg0EsweckXCJyNZv3tw8PD8eyZcvQsGFDyLIMk8mEhIQEHD58GH/++SdOnTqFR48eQZZlNGzYEGvWrEHbtm2dETt5OFdtYWDPCiVVLlwQAfXqZU5YAgOB774TGUA2gbpbdYNdmYnIE9hUaVGEhoZiyZIlOHXqFHbu3Injx4/j1q1bePjwIYoUKYJq1aqhefPmCMlSEifKavJkMWSTU8XF3pulU5bzmkzA118D48aJcR5Fjx5ig8MSJXK8jrtVN5SuzJGR4r2yFJMynDV3rof2yiEij2dX0qKoXLkyKleu7KhYyAepuVkaDCJhsWcLAy0TXi32yvnnH6B/f+D3383HSpcGvvoKCA+36TrOTthspXRl/uADy4meMpw1eLB4fPJkJi9E5Fo2Dw8ROZoztzBw2ITXtDTg449F35WMCUu/fsCxYzYnLIB77jmldGWeN0+8D5aGi7xqawUi8iiaKi2epG/fvjhw4AAOHDigdyhkgbO2MHDIhNdDh0Ry8uef5mMVKogholat7A8Olqsbfn4iBiVhmzTJtRWN+Hhg2LDs5wF5xdYKRORxfCJpmTFjBv744w+7Nnsk13L0FgaaVig9eCBm5U6fLiotyoOjRoksI39+h8TobntOef3WCkTksbw6aUlJScH777+P1atX6x0K6cTuCa+XdgFt+gHHj5sfrFEDWLgQePZZp8Wq955T3IeIiNyZV85pkWUZGzduROfOnbF69WqUK1dO75BIR7Yt55UxKe+nohOdkrDkygVMmQLs3++0hMVduFOnXiKirLwyabl06RJGjRqFy5cvo2/fvliwYIHeIZGOVE949TNhedHBCPtprPnOXb++mMvy/vti/yAv506deomIsvLK4aHcuXMjIiICAwcORIUKFXDx4kW9QyIdJCSIykFyspiQGxMDfPONpQmvMtqXOYhJFwYi7Po+8eSAADFvZdSo9P2CfIE7deolIsrKK/81LlmyJD766CO9wyCdxMeLfGP9+idX43ToICaNJiY+nvD6z59o8dMgBF3IsDKoWTOx4aEP9iBy1dYKRET2cPukZdCgQdi2bZuqc7ds2YKyZcs6NyByazEx5kZ11jZG3LgR+Gn+Lby+fSCwcqX5yQULAjNniuZxto6ReAl369RLRJSR2yctxYoVw9NPP63q3Fw+VManJ6neGBEyIvsXwE6cQ3p7kfbtgfnzASa9btepl4hI4fZ3+WnTpukdAnkI1f1FIEGGhChMwpri/YHZs4GePW3fwdBLOXtrBSIie/lmDZy8jtJfRM2QBgAYkQtr0REJv5wAXn6ZCUsWztxagYjIXm5faSFSw67+IvBD3KFieP0Z58Tk6dytUy8REZMW8gpKfxFbluuyv4g67tCpl4gIYNJCbiprj5WWLbP/dM/+IkRE3o9JC7mVnHqsTJ5seeKn6C8iQ5bVz01hfxEiIs/CibjkNmJixJY/Gzda77Hy3HPivKyCLG38+AAAG5dJREFULvyBDvm2woA0VdcyGICOHTk3g4jIk/hE0lK2bFn8/fffOHDggN6hkBUZe6xYWwGkPBYZCezd+/jg3bvAiBFA06aYfG/848XM2Y8Tsb8IEZFn8omkhdyf6h4rj8+JigKwaRMQGgp8+SUgywjDPvxUZTIMuaTsN0Y06NdfJCEBWLxYtIZZvFj8nYiI1GHSQrqzuceKEVgba0JCmwHmu37evMBnnyHi+IfYuVNyu/4i8fFiOCo4GOjbFxg9WnwNDgY6dcpQOSIiIqs4EZdUsXU1jy3s7rGCFngdS8Rs2m++ASpWBOB+/UVU74f0k2jqRkREljFpoWzZu5rHFnb1WIERd/xLAHO+Afr1s9jR1h36i6jeD0kS5+3cqW9bfGcmp94UExHpg0kLWeWqCoFdPVZgQKGPJgD9i9p/YRewZ67OmjWuiS0jVySn3hATEemLc1rIIrWredLSgB49tM3JED1WbHuOJMlo0dW9Exa75uqsdf3kXC1LzX0pJiLSH5MWskhthQAQN9s333zyuNqVMkFB4pOztRU/WYkeKyLLceeVOHbN1ZHFPBxXsXupuY/FRETugcND9ASlQmDLDXfvXlEl6NjRvrL+5MniU3VOXW2ViszNm2LljTsPG3jCfkjuOHzljjERkXtgpYWeYE+FAACmTLG/rB9W5xF+6r4SBjnNaldbg8GctOza5f7DBu6+H5I7Dl+5Y0xE5D6YtNATlAqBrQ4eFPNbbC7r798PhIUhYll37MRzaIcN6V1tM/ZYee458dVk8oxhA/vm6rhuPyR3HL5yx5iIyH0waaEn2FMhUJhMNpT13zcC77wDNGgAHDoEAAgzHEDs+J049/dDLF4MzJol5qucOwcUKWJ+vqrXj7Lve3AU++bquG45rz3JqbOHr9wxJiJyH5zTQk9QKgT2DBGpfY7RCKxdLyFh/Y8IwuOySe3awMKFQL16CALweoj5fFvn2WQcNtCzp4d5rk72seuxH5I7Dl+5Y0xE5D5YaaEnBAUBtWo5/zpKV1vkySPKInv3AvXqWTzXU4cNwsJEHxtlzyNL9NoPyR2Hr9wxJiJyH0xayKIPPnD+NfxgxJ3g2mIyzMSJQO7cVs/15GGDiAjR6dbd9kNyx+Erd4yJiNwHh4fIoo4dgfr1gX371J1v69Je4HFX28kjgeo5ZyOePmzgbvshKdxx+ModYyIi98Ckhaz66iugUaOcl59Kkn1JiyQBLVqpK5/YM8/GHYcN3GE/pIyU4StluwZLP2tlqbmrhq/cMSYicg8cHiKrwsLETSFXLutDMxnnY3Ts6LyyPocNnMcdh6/cMSYi0h8rLZQt5ebxwQfm1TsZO9C2by/K82FhQNmywMaNMiQA4n8ts7esz2ED53HH4St3jImI9MWkhXKk9uYRVuwMfqq2BJFHJkGGBKOFXy8tZX0OGzifuw1fAe4ZExHpg8NDpJpy8xgxQnxNT1iMRuDzz4GaNRFxZGq2XW21lvU5bEBE5LtYaSFtjh4F+vUD9uxJPxQWdA2xC/IgoYafU8r6HDYgIvJNTFrIPg8fAjNmiMkujx6Zjw8bBkybBhQsKLravu68EDhsQETkW5i0kO327hXVlb/+Mh8LCQGio4GmTfWLi4iIvBrntJB6KSnA228Dzz5rTlgMBmDCBLHhIRMWIiJyIlZaSJ1t24ABA4BTp8zH6tQRGxzWratbWERE5DtYaaHsJSUBgwcDL7xgTlj8/cW8lfh4JixEROQyrLSQdevXA4MGAZcumY81bizmrlSrpl9cRETkk1hpoSddvw68+qrom68kLPnzA19+Cfz+OxMWIiLSBSstZCbLwP/+J7rH3bhhPv7SS8CCBUD58vrFRkREPo+VFhIuXgQ6dQJeecWcsBQtCixZIjb8YcJCREQ6Y9Li60wm4OuvgdBQsSOiols34Phx4LXXzP3yiYiIdMThIV926pRYxrxtm/lYqVLA3Llikx8iIiI3wkqLL0pLA2bOBGrWzJywvPEGcOwYExYiInJLrLT4mr/+Ei349+41HwsOBr75BmjVSrewiIiIcsJKi6948AB47z3RDE5JWCQJGDlSJDJMWIiIyM2x0uIL9uwR1ZWjR83HqlcXLfgbNdIvLiIiIhuw0uLN7t0D3npLJCZKwpIrFzBpEnDgABMWIiLyKKy0eKstW8TKoLNnzcfq1RPVldq19YuLiIjITqy0eJvbt0Wy0qqVOWEJCABmzAB272bCQkREHouVFm+yZg0wZAhw5Yr5WNOmYoPDkBD94iIiInIAVlq8wbVrQM+eQHi4OWEpUAD46ivRh4UJCxEReQFWWjyZLAM//CCWLd+8aT7eti0wfz4QFKRfbERERA7GpMVTXbgADB4MbNhgPhYYCHzxBfDqq9wviIiIvA6HhzyNyQTMmyc2OMyYsERGig0Oe/ViwkJERF6JlRZPcvKkWBn0++/mY6VLiySmc2f94iIiInIBVlo8QVoa8PHHYrlyxoSlf3+xwSETFiIi8gGstLi7Q4eAvn2B/fvNxypWBL7+GmjZUr+4iIiIXMxrk5aTJ08iOjoa8fHxuHHjBgICAlC9enVERkaiQ4cOeoeXswcPgKgoYPp0UWkBAD8/YNQoYOpUIH9+feMjIiJyMa9MWuLi4jBixAg8evQI5cuXx/PPP4/ExETs27cP8fHx2L17N6KiovQO07q0NFFF+eMP87EaNYBFi4CGDfWLi4iISEdel7QkJydjwoQJePToEcaNG4e+fftCerya5tChQ+jXrx9WrFiB5557Du3atdM5WiuuXTMnLLlzA+++C0yYAPj76xsXERGRjrxuIu6vv/6K27dvo0GDBujXr196wgIAtWvXxuDBgwEAsbGxeoWYs9KlgU8/FSuF/vwT+O9/mbAQEZHP87pKy6NHjxAaGormzZtbfLxixYoAgGvXrrkwKhtJEvDWW3pHQURE5Fa8LmmJjIxEZGSk1ccPHToEAChVqpSrQiIiIiIH8LrhoexcvXoV3333HQC473wWIiIissjtKy2DBg3Ctm3bVJ27ZcsWlC1b1uJjycnJGDp0KO7du4ewsDC0b9/egVESERGRs7l90lKsWDE8/fTTqs7Nlcvyt5OYmIgBAwbg6NGjKFu2LD7//PNME3SJiIjI/bl90jJt2jRNzz958iSGDBmCixcvokKFCli8eDGKFy/uoOiIiIjIVbx6Tstvv/2Gnj174uLFi6hbty6WLVuG0qVL6x0WERER2cFrk5affvoJQ4YMwb1799CpUycsWbIERYsW1TssIiIispPbDw/ZY/Xq1XjvvfcgyzKGDx+OYcOG6R0SERERaeR1lZYzZ84wYSEiIvJCXldpmTt3LlJTU5E7d26cPXsWY8eOtXhe6dKlMWbMGBdHR0RERPaSZFmW9Q7CkerVq4e7d+/meF6VKlWwbt06h1yzQYMGSEpKQkBAACpVquSQ1yQiIvIFp0+fRmpqKgoXLoz4+Phsz/W6pEUPtWvXRmpqqt5hEBEReayAgID0rXas8brhIT0EBgbi5s2b8Pf3t9qRl4iIiJ508eJFPHjwAIGBgTmey0oLEREReQSvWz1ERERE3olJCxEREXkEJi1ERETkEZi0EBERkUdg0kJEREQegUkLEREReQQmLUREROQRmLQQERGRR2DSQkRERB6BSQsRERF5BCYtRERE5BGYtBAREZFHYNJCREREHoFJCxEREXkEJi1ERETkEZi0uImTJ09i3LhxaN68Of7zn/+gfv366N27N9atW6d3aD6vb9++eOaZZ/QOw+udPXsWY8eOxQsvvIBatWrhxRdfxKxZs5CSkqJ3aD7v3LlzqFOnDqZOnap3KD5rzZo16N27N8LCwvCf//wHzZo1w/jx43H69Gm9Q3MpJi1uIC4uDhEREVizZg3y5MmD559/HpUqVcK+ffswZswYTJo0Se8QfdaMGTPwxx9/6B2G1zt8+DAiIiKwdu1aFC9eHM2bN0dKSgrmz5+Pnj174u7du3qH6LNu3LiBoUOH4v79+3qH4pNkWcaYMWMwbtw47N+/H5UqVcLzzz8Pg8GA1atXIyIiAjt27NA7TNeRSVd37tyRGzRoIIeEhMjR0dGyyWRKf+zgwYNyvXr15JCQEHn9+vU6Rul77t27J48bN04OCQmRQ0JC5Dp16ugdktd69OiR3LJlSzkkJEResWJF+vH79+/LgwcPlkNCQuT3339fxwh917Fjx+TWrVun/3fAn4PrrV69Wg4JCZEbN24sHz9+PP14Wlqa/Nlnn8khISFyo0aN5Lt37+oYpeuw0qKzX3/9Fbdv30aDBg3Qr18/SJKU/ljt2rUxePBgAEBsbKxeIfoUWZaxceNGdO7cGatXr0a5cuX0DsnrrV+/HhcuXECjRo3QrVu39OMBAQGYNm0a8uXLh+XLlyMpKUnHKH1LUlISPvnkE/To0QPnz59H2bJl9Q7JZ61cuRIAMGbMGFSrVi39uMFgwKhRo1ClShUkJib6TEWYSYvOHj16hNDQUDRv3tzi4xUrVgQAXLt2zYVR+a5Lly5h1KhRuHz5Mvr27YsFCxboHZLXi4uLAwC0bt36iceKFi2Khg0b4tGjR9i+fburQ/NZS5cuRXR0NAIDAzFv3jyEh4frHZLPKlSoECpVqoT69es/8ZgkSahQoQIA4OrVq64OTRe59A7A10VGRiIyMtLq44cOHQIAlCpVylUh+bTcuXMjIiICAwcORIUKFXDx4kW9Q/J6J0+eBABUrVrV4uOVK1fG1q1bceLECXTo0MGVofmsUqVKYfz48XjllVcQEBCAo0eP6h2Sz5o7d67Vx4xGY/rPpnTp0q4KSVdMWtzY1atX8d133wEA2rVrp3M0vqFkyZL46KOP9A7DpyhVxJIlS1p8vESJEpnOI+fr3r273iGQCj/++CMuXbqEIkWKoFGjRnqH8//t3XtQVPX7B/D3qqtcDUGbuAiieFbJwsskTqCoQSQm0wULw4pRWwOjNEsrDRoxLJlRg7zEQIlBZGijI+aQ5iUYEcKsGdSBEHFERySTq67A7uf3h7Pny/7YFbztuu77NcPMcj635+wq88w5z+esWTBpuccWLlyIw4cP96rvb7/9ZvJecUtLC+Lj49HW1oannnoKM2fOvIdR2oZ79VnQ/aXf0mxnZ2e0XX+cW5+J/qekpARr164FAHzwwQdwdHS0cETmwaTlHnNzc4Onp2ev+vbrZ/ztv3LlCt566y2cPHkSXl5e2LBhg0GBLvXOvfgs6P7r27cvdDpdj//GhRBmiojowXbo0CEsXrwY7e3tmDNnjk1dGeNf6nssJSXlrsZXVVUhLi4OdXV18PX1xXfffYfBgwffo+hsy91+FmQejo6OaGxsNPkcEI1GAwCwt7c3Z1hED6Tvv/8ea9asgVarRUxMDD799FNLh2RW3D30ADly5Aiio6NRV1eH8ePHIy8vz2aKq8h26WtWGhoajLbra1n0/YhsUWdnJxITE7F69WrodDosWbIEiYmJNncVnknLA2L79u2Ii4tDW1sbIiMjkZ2djUGDBlk6LKL7Tr9rqLq62mi7/rip3UVEDzuNRoOFCxdi+/btsLe3x4YNG+RneNkaJi0PgF27diEpKQlarRYJCQlITU1F//79LR0WkVmEhIQAAAoLC7u1Xb16FaWlpVAqlQgKCjJ3aEQWp9VqsWjRIhQXF8PNzQ3btm3Dc889Z+mwLIZJi4XV1NQgKSkJQggkJCTgnXfesXRIRGYVFhYGDw8PFBcXIzc3Vz6u0WiwYsUKXLt2DVFRUaztIpu0efNmFBcXw8HBAdnZ2XjyySctHZJFsRDXwjZu3AiNRgOlUil/y60x7u7uWLp0qZmjI7r/7Ozs8MUXX0CtVmPVqlXYuXMnvLy8cOLECVy+fBn+/v4m/18QPcyampqQlZUF4GZN162e0D1r1iz5quXDjEmLhemfI9LR0YGCggKT/UaOHMmkhR5agYGByM/Px9dff42ysjJUV1fDy8sLUVFRmD9/PpycnCwdIpHZlZWVyc8nqq2tRW1trcm+o0ePtomkRSH48AMiIiKyAqxpISIiIqvApIWIiIisApMWIiIisgpMWoiIiMgqMGkhIiIiq8CkhYiIiKwCkxYiIiKyCkxaiIiIyCowaSEiIiKrwKSFiAzU1dVBpVKZ/BkzZgwmTZqE6OhobNmyBa2trZYOGQBQWloqx9jZ2SkfT09Ph0qlwpw5c+7JOtevX0ddXZ3BsZ9//hkqlQpTpky5J2sQkXFMWojIJEmSMH78eIOfUaNGwcHBASdOnMD69esxa9YsnDt3ztKhmsWePXsQHh6OkpISS4dCZJP4hYlEZNLKlSsRGBhotK20tBTx8fG4ePEili9fjh9//NHM0fVOTEwMIiIiYG9vf9dzrV+/HvX19d2Oh4WFISAgAEql8q7XICLTeKWFiO5IYGAg3n//fQDAiRMnUFFRYeGIjHN1dcWIESPg4eFx39ZwdnbGiBEj4O3tfd/WICImLUR0F8LCwuTXf//9twUjISJbwKSFiO6Ys7Oz/LqtrQ0A8Prrr0OlUuHIkSPYuHEjnn76aQQEBOD555/HmTNn5P7//vsv1q5di4iICAQEBGDcuHF4+eWX8e233+LGjRsm1ywtLcXbb7+N4OBgBAQEICoqCgUFBSb791SIe/DgQcTFxWHKlCkYM2YMgoODsXjxYoMrR/o5Lly4AODmbTOVSoX09HQAPRfilpSUICEhAcHBwXIh84IFC/Drr78a7T99+nSoVCqcOXMGZWVlUKvVCAwMxBNPPIEZM2YgLS1Nfr+JbAlrWojojnUtwH3ssccM2rZs2YI///wT3t7ecHZ2RmtrK4YNGwYAOH78OOLj49HY2AilUolhw4ZBCIGTJ0+ioqICu3fvRmZmJoYMGWIwZ0ZGBtatWwchBNzc3ODn54fa2losXboUEydOvK3YtVotPv74Y+zevRsAMGTIEEiShPPnz2Pfvn3Yv38/Nm3ahJCQELi7u2P8+PGoqKhAe3s7fHx84ObmBnd39x7XSU5ORk5ODgDAxcUFo0aNQn19PYqKilBUVIQZM2YgNTXVaD1Mfn4+tm7div79+2PYsGFoampCTU0NNm7ciKNHjyI3Nxd9+/a9rfMmsmqCiKiL8+fPC0mShCRJ4tixY7fsu2zZMiFJknj88cdFQ0ODEEKIuXPnyuMzMjLkvleuXBFCCHHp0iUxceJEIUmSWLlypWhqapL7nDt3TsyePVtIkiRee+01g7XKy8uFJElCpVKJrKwsodVqhRBCaDQakZycLK8pSZLo6OiQx6WlpQlJkkR0dLTBfN98842QJEkEBASIgoICodPp5PmSkpKEJEli7NixorGxUR4zbdo0IUmS+Omnnwzm2rlzp5AkSUyePNngeFZWlpAkSfj7+4ucnBw5ZiGE+OWXX8TYsWOFJEkiOTnZYJx+HUmSxEcffSSam5uFEELodDqRk5Mjt+3fv9/kZ0P0MOLtISK6LRqNBqdOnUJSUhJ27doFAIiNjcXgwYMN+nl6emLBggXy766urgCArKwsNDY2Yvr06UhOTsbAgQPlPt7e3ti0aROcnJxQXl6OI0eOyG2bN28GALz44ouYN28e+vS5+edrwIABWLlyJSZNmtTrc2hvb0dGRgYAYNmyZZg5cyYUCoU8X2JiInx9fXHt2jXs27ev1/N2dePGDTnmd999FzExMXLMADBjxgysXr0aAPDDDz90e/YLAIwaNQopKSnybTiFQoGYmBioVCoAN69YEdkS3h4iIpPeeOONHvvMnj0b7733Xrfj48aNkxOBrg4cOAAAiIyMNDrf4MGDERQUhMLCQhw6dAghISG4fv06SktLAdxMWoyJjo7GsWPHeowXAMrLy9HS0gKlUomXXnqpW3ufPn2QkZEBpVLZ7bZXb5WXl6O5uRn9+vVDTEyM0T4RERH48ssvUV9fj8OHD2Pu3LkG7VOnTjX6Hg4fPhyVlZVoaWm5o9iIrBWTFiIySZIkODk5yb8rFAoMGDAALi4uUKlUCA0NhZ+fn9Gx/78eBbhZrKsvZt20aRO2bdtmdKy+T01NDQDg4sWLaG9vBwCMHDnS6JjRo0f38qz+V4vj6+sLOzs7o33udvuyPnYfHx+D97ArhUIBf39/1NfX4+zZs93aH330UaPj9DFrtdq7ipHI2jBpISKTbvVwuZ4MGDCg27Guj/yvqqrqcQ79lYSmpib5mKOjo9G+XW8z9aSxsREA4ODg0Osxt0t/rl13WBmjT2iM7Qbq37//LccKIe4wOiLrxKSFiMym61Np9+zZA0mSejXOxcVFft3a2irXx3R1q23SpuK4n9uG9clVT7dwmpubDfoTkWksxCUisxk4cKBcsFtdXW2yX2VlJU6fPi1fYfHw8JBviZw6dcromH/++afXcfj6+gK4eZvIVLKTl5eH2NhYZGVl9XreroYPHy6vYepLJXU6nXw+Pj4+d7QOkS1h0kJEZjV16lQAQE5ODnQ6Xbf2lpYWvPnmm3jhhReQnZ0N4GYNh/7BbXl5eUbnzc/P73UMEyZMgIODA9rb27Fnz55u7TqdDjt27EBJSQmuXbsmH9cXxfbmtsyECRPwyCOPoLOzE7m5uUb77N27Fw0NDVAoFJg8eXKv4yeyVUxaiMis1Go1HBwccPz4cXz44Yf477//5LYLFy5ArVbj6tWrcHZ2Nth1k5CQAKVSiQMHDiA1NVUuzO3o6MBXX31l8umyxjg5OSE2NhYAsGbNGhw8eFBu02g0+Pzzz1FRUQEnJye8+uqrcpu+BkZfKHwr9vb2UKvVAIC0tDTk5uYaJGmFhYVITEwEALzyyivy1R8iMo01LURkVj4+PtiwYQOWLFmCgoICFBYWws/PDx0dHaitrUVnZyccHByQkZEBNzc3eZwkSUhJScEnn3yCzMxM5Ofnw9vbG+fPn0djYyPCwsKwf//+XsexaNEinD17Fvv27UNcXBzc3d3h6uqK2tpatLW1wc7ODuvWrTPYwePv74+qqipkZmbi999/R1hYGOLj402uMX/+fNTV1SEvLw+rVq1Ceno6hg4dikuXLuHy5csAgPDwcKxYseIO3kki28OkhYjMLiQkBHv37sXWrVtRVFSEs2fPQqvVwtPTE0FBQZg3bx6GDh3abVxkZCRGjhyJzMxM/PHHH6isrISPjw8SEhLwzDPP3FbS0q9fP6xfvx7PPvssduzYgZMnT6KyshJubm4IDw+HWq3udvVj+fLluH79Oo4ePYqamhqD71IyRqFQ4LPPPkNoaCjy8vLw119/4fTp0xg0aBCmTZuGqKgohIaG9jpmIlunENwzR0RERFaANS1ERERkFZi0EBERkVVg0kJERERWgUkLERERWQUmLURERGQVmLQQERGRVWDSQkRERFaBSQsRERFZBSYtREREZBWYtBAREZFVYNJCREREVoFJCxEREVkFJi1ERERkFf4PQAY1hT4m3q4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "y_range = np.linspace(Y_v.min(), Y_v.max(), 50)\n",
    "ax.plot(y_range, y_range, 'r', lw=2)\n",
    "ax.plot(Y_v, m_v, 'bo')\n",
    "ax.set_xlabel('Prediction')\n",
    "ax.set_ylabel('Observation');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical diagnostics\n",
    "\n",
    "Statistical diagnostics compare the predictive distribution to the distribution of the validation dataset.\n",
    "The way to start, are the standarized errors defined by:\n",
    "$$\n",
    "e_i = \\frac{y_i^v - m_n\\left(\\mathbf{x}^v_i\\right)}{\\sigma_n\\left(\\mathbf{x}^v_i\\right)}.\n",
    "$$\n",
    "Now, if our model is correct, the standarized errors must be distributed as a standard normal $N(0,1)$ (why?).\n",
    "There are various plots that you can do to test that.\n",
    "First, the histogram of the standarized errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Std. error')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_v = np.sqrt(v_v)\n",
    "e = (Y_v - m_v) / s_v\n",
    "fig, ax = plt.subplots(dpi=100)\n",
    "zs = np.linspace(-3.0, 3.0, 100)\n",
    "ax.plot(zs, st.norm.pdf(zs))\n",
    "ax.hist(e, density=True, alpha=0.25)\n",
    "ax.set_xlabel('Std. error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Close, but not perfect.\n",
    "Another common plot is this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.plot(e, 'o')\n",
    "ax.plot(np.arange(e.shape[0]), 2.0 * np.ones(e.shape[0]), 'r--')\n",
    "ax.plot(np.arange(e.shape[0]), -2.0 * np.ones(e.shape[0]), 'r--')\n",
    "ax.set_xlabel('$i$')\n",
    "ax.set_ylabel('$e_i$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where the red lines indicate the 95% quantiles of the standard normal.\n",
    "This  means that if 5\\% of the errors are inside, then we are good to go.\n",
    "\n",
    "Yet another plot yielding the same information is the q-q plot comparing the empirical quantiles of the standarized errors to what they are supposed to be, i.e., to the quantiles of $N(0,1)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "st.probplot(e.flatten(), dist=st.norm, plot=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note on Gaussian process diagnostics\n",
    "\n",
    "For a more detailed description of GP regression diagnostics, please see this [paper](https://www.jstor.org/stable/40586652)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "+ Experiment with larger number of training points $n$. Are the models becoming better according to the metrics we defined above?\n",
    "+ Experiment with smaller measurement noises $\\sigma$. What do you observe? Which diagnostics make sense for very small $\\sigma$'s?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibrating the Hyperparameters of a Gaussian Process\n",
    "\n",
    "So, we saw how GP regression works but everything we did was conditional on knowing the hyperparameters of the covariance function, we called them $\\theta$, and the likelihood variance $\\sigma^2$.\n",
    "But if what do we do if we are not sure about them?\n",
    "We will do what we always do:\n",
    "\n",
    "+ We summarize our state of knowledge about them by assigning prior probability density $p(\\theta)$ and $p(\\sigma)$.\n",
    "\n",
    "+ We use the Bayes rule to derive our posterior state of knowledge about them:\n",
    "$$\n",
    "\\begin{array}{ccc}\n",
    "p(\\theta,\\sigma | \\mathcal{D}) &\\propto& p(\\mathcal{D}|\\theta,\\sigma)p(\\theta)p(\\sigma) \\\\\n",
    "&=& \\int p(\\mathbf{y}_{1:n}|\\mathbf{f}_{1:n},\\sigma) p(\\mathbf{f}_{1:n} | \\mathbf{x}_{1:n},\\theta)d\\mathbf{f}_{1:n} p(\\theta)p(\\sigma).\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "+ We somehow approximate this posterior. So far, we only know of one way of approximating this posterior, and that is by a maximum a posteriori estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making a little bit of analytical progress in the posterior\n",
    "We stated without proof that the posterior of the hyperparameters is:\n",
    "$$\n",
    "p(\\theta,\\sigma|\\mathcal{D}) \\propto \\int p(\\mathbf{y}_{1:n}|\\mathbf{f}_{1:n},\\sigma)p(\\mathbf{f}_{1:n}|\\mathbf{x}_{1:n},\\theta)d\\mathbf{f}_{1:n}p(\\theta)p(\\sigma).\n",
    "$$\n",
    "You should ry to familiriaze yourself with these expressions.\n",
    "How can you just see the validity of these expressions?\n",
    "It's quite simple if you look at the graph.\n",
    "So, let's draw the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: gp Pages: 1 -->\n",
       "<svg width=\"170pt\" height=\"188pt\"\n",
       " viewBox=\"0.00 0.00 170.00 188.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
       "<title>gp</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-184 166,-184 166,4 -4,4\"/>\n",
       "<!-- sigma -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>sigma</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"23\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">σ</text>\n",
       "</g>\n",
       "<!-- y1n -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>y1n</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"63\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"51.5\" y=\"-15.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">y</text>\n",
       "<text text-anchor=\"start\" x=\"59.5\" y=\"-15.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">1:n</text>\n",
       "</g>\n",
       "<!-- sigma&#45;&gt;y1n -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>sigma&#45;&gt;y1n</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M35.7146,-72.5708C39.9597,-64.0807 45.1536,-53.6929 49.8663,-44.2674\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"53.024,-45.7782 54.3657,-35.2687 46.763,-42.6477 53.024,-45.7782\"/>\n",
       "</g>\n",
       "<!-- theta -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>theta</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"63\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"59\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">θ</text>\n",
       "</g>\n",
       "<!-- f -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>f</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"89\" y=\"-87.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">f</text>\n",
       "<text text-anchor=\"start\" x=\"94\" y=\"-87.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">1:n</text>\n",
       "</g>\n",
       "<!-- theta&#45;&gt;f -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>theta&#45;&gt;f</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M71.7146,-144.5708C75.9597,-136.0807 81.1536,-125.6929 85.8663,-116.2674\"/>\n",
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       "</g>\n",
       "<!-- x1n -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>x1n</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"135\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"123.5\" y=\"-159.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "<text text-anchor=\"start\" x=\"131.5\" y=\"-159.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">1:n</text>\n",
       "</g>\n",
       "<!-- x1n&#45;&gt;f -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>x1n&#45;&gt;f</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M126.2854,-144.5708C122.0403,-136.0807 116.8464,-125.6929 112.1337,-116.2674\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"115.237,-114.6477 107.6343,-107.2687 108.976,-117.7782 115.237,-114.6477\"/>\n",
       "</g>\n",
       "<!-- f&#45;&gt;y1n -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>f&#45;&gt;y1n</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M90.2854,-72.5708C86.0403,-64.0807 80.8464,-53.6929 76.1337,-44.2674\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.237,-42.6477 71.6343,-35.2687 72.976,-45.7782 79.237,-42.6477\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1a29234110>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g3 = Digraph('gp')\n",
    "g3.node('sigma', label='<&sigma;>')\n",
    "g3.node('theta', label='<&theta;>')\n",
    "g3.node('x1n', label='<<b>x</b><sub>1:n</sub>>', style='filled')\n",
    "g3.node('f', label='<<b>f</b><sub>1:n</sub>>')\n",
    "g3.node('y1n', label='<<b>y</b><sub>1:n</sub>>', style='filled')\n",
    "g3.edge('theta', 'f')\n",
    "g3.edge('x1n', 'f')\n",
    "g3.edge('f', 'y1n')\n",
    "g3.edge('sigma', 'y1n')\n",
    "g3.render('gp_reg3', format='png')\n",
    "g3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph, tells you how the joint distribution of all the variables decomposes in conditional probabilities.\n",
    "You know that the parent nodes condition the children nodes.\n",
    "Here is the decomposition here:\n",
    "$$\n",
    "p(\\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}, \\mathbf{f}_{1:n}, \\theta, \\sigma) =\n",
    "p(\\mathbf{y}_{1:n} | \\mathbf{f}_{1:n}, \\sigma) p(\\mathbf{f}_{1:n} | \\mathbf{x}_{1:n}, \\theta)p(\\theta)p(\\sigma)p(\\mathbf{x}_{1:n}).\n",
    "$$\n",
    "Now, by Bayes' rule, we know that the conditional joint probability density of all unobserved variables is proportional to the joint:\n",
    "$$\n",
    "p(\\theta, \\sigma, \\mathbf{f}_{1:n} | \\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}) \\propto p(\\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}, \\mathbf{f}_{1:n}, \\theta, \\sigma).\n",
    "$$\n",
    "The normalization constant does not matter, i.e., we can drop $p(\\mathbf{x}_{1:n})$, so we get:\n",
    "$$\n",
    "p(\\theta, \\sigma, \\mathbf{f}_{1:n} | \\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}) \\propto p(\\mathbf{y}_{1:n} | \\mathbf{f}_{1:n}, \\sigma) p(\\mathbf{f}_{1:n} | \\mathbf{x}_{1:n}, \\theta)p(\\theta)p(\\sigma).\n",
    "$$\n",
    "Finally, to get the posterior over $\\theta$ and $\\sigma$ only, we *marginalize* (i.e., integrate out) the unobserved variable $\\mathbf{f}_{1:n}$.\n",
    "Here, the integral is actually analytically available (integral of a Gaussian times a Gaussian which is a Gaussian).\n",
    "If you do the math, you will get:\n",
    "$$\n",
    "p(\\theta,\\sigma | \\mathcal{D}) \\propto \\mathcal{N}\\left(\\mathbf{y}_{1:n}\\middle|\n",
    "\\mathbf{m}(\\mathbf{x}_{1:n}), \\mathbf{K}(\\mathbf{x}_{1:n},\\mathbf{x}_{1:n}) + \\sigma^2\\mathbf{I}_n\\right) p(\\theta)p(\\sigma).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum a Posteriori Estimate of the Hyperparameters\n",
    "\n",
    "In the maximum a posteriori estimate (MAP) we are basically approximating the posterior with the $\\delta$-function centered at its pick.\n",
    "That is, we are approximating:\n",
    "$$\n",
    "p(\\theta,\\sigma|\\mathcal{D}) \\approx \\delta(\\theta-\\theta^*)\\delta(\\sigma-\\sigma^*),\n",
    "$$\n",
    "where $\\theta^*$ and $\\sigma^*$ are maximizing $\\log p(\\theta,\\sigma|\\mathcal{D})$.\n",
    "It is instructive to see what $\\log p(\\theta,\\sigma|\\mathcal{D})$ looks like and see if we can assign any intuitive meaning to its terms.\n",
    "It is:\n",
    "$$\n",
    "\\begin{array}{ccc}\n",
    "\\log p(\\theta,\\sigma|\\mathcal{D}) &=& \\log \\mathcal{N}\\left(\\mathbf{y}_{1:n}\\middle|\n",
    "\\mathbf{m}(\\mathbf{x}_{1:n}), \\mathbf{K}(\\mathbf{x}_{1:n},\\mathbf{x}_{1:n}) + \\sigma^2\\mathbf{I}_n\\right) + \\log p(\\theta) + \\log p(\\sigma) \\\\\n",
    "&=& \n",
    "-\\frac{1}{2}\\left(\\mathbf{y}_{1:n}-\\mathbf{m}(\\mathbf{x}_{1:n})\\right)^T\\left(\\mathbf{K}(\\mathbf{x}_{1:n},\\mathbf{x}_{1:n}) + \\sigma^2\\mathbf{I}_n\\right)^{-1}\\left(\\mathbf{y}_{1:n}-\\mathbf{m}(\\mathbf{x}_{1:n})\\right)\\\\\n",
    "&&-\\frac{1}{2}\\log |\\mathbf{K}(\\mathbf{x}_{1:n},\\mathbf{x}_{1:n}) + \\sigma^2\\mathbf{I}_n|\\\\\n",
    "&&+\\log p(\\theta) + \\log p(\\sigma)\\\\\n",
    "&& + \\text{constants}.\n",
    "\\end{array}\n",
    "$$\n",
    "The constants are terms that do not depend on $\\theta$ or $\\sigma$.\n",
    "The first term is a familiar one.\n",
    "It kind of looks like least squares (it is actually a form of least squares).\n",
    "The third and forth term are familiar regularizers stemming from our prior knowledge.\n",
    "The second term is a naturally occuring regularizer.\n",
    "\n",
    "Now, back to solving the optimization problem that yields the MAP.\n",
    "Of course, you need to get the deratives of $\\log p(\\theta,\\sigma|\\mathcal{D})$ and use an optimization algorithm.\n",
    "Back in the stone age, we were doing this by hand.\n",
    "Now you don't have to worry about it.\n",
    "Automatic differentiation can work through the entire expression (including the matrix determinant).\n",
    "Once you have the derivative you can use a gradient-based optimization algorithm from [scipy.optimize](https://docs.scipy.org/doc/scipy/reference/optimize.html).\n",
    "``GPy`` is using by default the [L-BFGS algorithm](https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html) but you could change it if you want.\n",
    "These are minimization algorithms.\n",
    "So, ``GPy`` is actually minimizing $-\\log p(\\theta,\\sigma)$.\n",
    "Let's see how it works through our previous example:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Gaussian process regression with fitted hyperparameters\n",
    "\n",
    "Make sure that you still have the data from the previous example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fixing the seed so that we all see the same data\n",
    "np.random.seed(1234)\n",
    "n = 10\n",
    "# The inputs are in [0, 1]\n",
    "X = np.random.rand(n, 1) # Needs to be an n x 1 vector\n",
    "# The outputs are given from a function plus some noise\n",
    "# The standard deviation of the noise is:\n",
    "sigma = 0.4\n",
    "# The true function that we will try to identify\n",
    "# Some data to train on\n",
    "Y = f_true(X) + sigma * np.random.randn(X.shape[0], 1)\n",
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's pick a squared exponential kernel and make a model with Gaussian likelihood (the default choice):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 13.029643687983668\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |  value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |    1.0  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |    1.0  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "k = GPy.kern.RBF(1) # GPy.kern.RBF(60, ARD=True)\n",
    "gpm = GPy.models.GPRegression(X, Y, k)\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's explain what all this means.\n",
    "Notice that there are some default values for the hyperparameters (they are all one).\n",
    "Also, notice that ``GPy`` is keeping track of how many parameters it needs to fit.\n",
    "Here we have three parameters ($s,\\ell$ and $\\sigma$).\n",
    "The second column are constraints for the parameters.\n",
    "The ``+ve`` term means that the corresponding hyperparamer has to be positive.\n",
    "Notice that there is nothing in the ``priors`` column.\n",
    "This is because we have set no priors right now.\n",
    "When this happens, ``GPy`` assumes that we assign a flat prior, i.e., here it assumes that we have assigned $p(\\theta)\\propto 1$ and $p(\\sigma)\\propto 1$.\n",
    "That's not the best choice, but it should be ok for now.\n",
    "\n",
    "Now, pay attention to the ``Objective``. This is the $-\\log p(\\theta,\\sigma|\\mathcal{D})$ for the current choice of parameters.\n",
    "Let's now find the MAP:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3201b82106ea4e70902a89a6db52f333",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 1/10, f = 9.376317801621127\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a8fe4faa4cae4dd3b410ee3d9b751c2a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 2/10, f = 9.376317801620589\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "71bb4201517f4d88b71f5cd9efdce170",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 3/10, f = 9.37631780162092\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d5db3be58339482b895a87a04e4b74a6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 4/10, f = 9.376317801620237\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6c350b3c6fc14dde8151ae08cb71ae0e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 5/10, f = 9.376317801668552\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b6e8450269414615b31af260097b963c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 6/10, f = 9.376317801620264\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a1d238e503284c90b5aeb1989a9dbf98",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 7/10, f = 9.376317801620694\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d13b4216422f44b79d340bb79729f427",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 8/10, f = 9.818938591239164\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "62f0f138c8b745c1837160be3848ddb3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 9/10, f = 9.376317801776946\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a9abe46a6baf4498ad47936e8e7b3dc8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 10/10, f = 9.376317801620374\n",
      "\n",
      "Name : GP regression\n",
      "Objective : 9.376317801620237\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 3\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   0.4296553390956265  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  0.02348797094550619  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.07952057754949901  |      +ve      |        \n"
     ]
    }
   ],
   "source": [
    "gpm.optimize_restarts(messages=True) # we use multiple restarts to avoid being trapped to a local minimum\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok. We did find something with higher posterior value.\n",
    "Let's plot the prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "m_star, v_star = gpm.predict(x_star)\n",
    "f_lower = m_star - 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "f_upper = m_star + 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "y_lower = m_star - 2.0 * np.sqrt(v_star)\n",
    "y_upper = m_star + 2.0 * np.sqrt(v_star)\n",
    "ax.fill_between(x_star.flatten(), y_lower.flatten(), y_upper.flatten(), color='red', alpha=0.25, label='$y^*$ 95% pred.')\n",
    "ax.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5, label='$f(\\mathbf{x}^*)$ 95% pred.')\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "ax.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Admitidly, this doesn't look very good.\n",
    "(Of course, we can tell this only because we know the truth).\n",
    "It seems that the assign lengthscale is too small.\n",
    "Also, the likelihood variance seems smaller than it really is.\n",
    "What do we do now?\n",
    "You have two choices:\n",
    "+ You encode some prior knowledge and repeat.\n",
    "+ You add some more data and repeat.\n",
    "\n",
    "Let's start with some prior knowledge and let the other item for the questions section.\n",
    "Let's say that we know that the noise variance.\n",
    "How do we encode this?\n",
    "Here you go:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 9.649326370937093\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 2\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   0.4296553390956265  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  0.02348797094550619  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.16000000000000003  |   +ve fixed   |        \n"
     ]
    }
   ],
   "source": [
    "gpm.likelihood.variance.constrain_fixed(sigma ** 2)\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that it now ``GPy`` reports that the likelihood variance is fixed.\n",
    "Let's repeat the optimization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ddc3b3e2fdd74155ae0ea32f1cc83c0d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 1/10, f = 9.574736850990455\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b6239ac2b3aa4b8682bdad0f3998d952",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 2/10, f = 9.57473685100571\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a67a49a333c64bdcb042099b79c92cfc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 3/10, f = 9.57473685099041\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ee43e20b66004b818d4302d66d16b2c9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 4/10, f = 9.574736851043617\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "60e7d28da15e42338e7c215ae19d8feb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 5/10, f = 9.57473685099096\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6cc7439801b94dce9676ff5f0670866c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 6/10, f = 9.574736850990337\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6e32f7c5ac8d4d5b97dbfb6881110d67",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 7/10, f = 9.57473685099032\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3bb2dfedeedf47529b4894ec092fcbfb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 8/10, f = 9.574736851031567\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "31e1928ff142485b9bdb24ba881dff77",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 9/10, f = 9.574736851005412\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ea3b164cd14443a5831295871c00906b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 10/10, f = 9.574736850990359\n",
      "\n",
      "Name : GP regression\n",
      "Objective : 9.57473685099032\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 2\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |  priors\n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   0.4079237022770511  |      +ve      |        \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  0.05041723327271677  |      +ve      |        \n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.16000000000000003  |   +ve fixed   |        \n"
     ]
    }
   ],
   "source": [
    "gpm.optimize_restarts(messages=True) # we use multiple restarts to avoid being trapped to a local minimum\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "m_star, v_star = gpm.predict(x_star)\n",
    "f_lower = m_star - 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "f_upper = m_star + 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "y_lower = m_star - 2.0 * np.sqrt(v_star)\n",
    "y_upper = m_star + 2.0 * np.sqrt(v_star)\n",
    "ax.fill_between(x_star.flatten(), y_lower.flatten(), y_upper.flatten(), color='red', alpha=0.25, label='$y^*$ 95% pred.')\n",
    "ax.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5, label='$f(\\mathbf{x}^*)$ 95% pred.')\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "ax.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks better.\n",
    "But it seems that the automatically selected lengthscale is smaller than the true one.\n",
    "(Of course don't really know the true lengthscale is).\n",
    "Let's assign a prior probability density on the lengthscale which pushes it to be greater.\n",
    "Since we are dealing with a positie parameter and we don't know much about it, let's assign an exponential prior with a rate of 2 (which will yield an expectation of 0.5):\n",
    "$$\n",
    "\\ell \\sim \\operatorname{Log-N}(0.2, 1).\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a27bb5c50>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ell_prior = GPy.priors.LogGaussian(.2, 1.0)\n",
    "# Let's visualize it to make sure it's ok\n",
    "fig, ax = plt.subplots(dpi=100)\n",
    "ells = np.linspace(0.01, 2.0, 100)\n",
    "ax.plot(ells, ell_prior.pdf(ells))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here is how you can set it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "reconstraining parameters GP_regression.rbf.lengthscale\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name : GP regression\n",
      "Objective : 15.598608334275422\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 2\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |    priors   \n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   0.4079237022770511  |      +ve      |             \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  0.05041723327271677  |      +ve      |  lnN(0.2, 1)\n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.16000000000000003  |   +ve fixed   |             \n"
     ]
    }
   ],
   "source": [
    "gpm.kern.lengthscale.set_prior(ell_prior)\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "59b117ec9ef041eb890038ce08d17a57",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 1/10, f = 12.755925770647497\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "311a352eadd546daaff8f244965362fb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 2/10, f = 12.755925770655134\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d7607b14743f4368ba5cc96904e13fae",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 3/10, f = 12.75592577066455\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "33984008d17d42b189e4eefec1e87ae0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 4/10, f = 12.755925770647167\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dffb65cb1bf447db8710327800d34c7e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 5/10, f = 12.755925770651487\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7d48a1a521db4dbab03513710d286a74",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 6/10, f = 12.755925770647178\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "04c11e9f5a594fe3a4d38c6015fa34c9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 7/10, f = 12.755925770648442\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7a48d86dbd0b460494d76035d2823080",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 8/10, f = 12.755925770648272\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "73f05c0c8b504a6a90401039f1f28efa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 9/10, f = 12.755925770647508\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ff4fca5e1b544c0d98e60de3729a8f36",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(IntProgress(value=0, max=1000), HTML(value=''))), Box(children=(HTML(value=''),)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 10/10, f = 12.7559257706584\n",
      "\n",
      "Name : GP regression\n",
      "Objective : 12.755925770647167\n",
      "Number of Parameters : 3\n",
      "Number of Optimization Parameters : 2\n",
      "Updates : True\n",
      "Parameters:\n",
      "  \u001b[1mGP_regression.         \u001b[0;0m  |                value  |  constraints  |    priors   \n",
      "  \u001b[1mrbf.variance           \u001b[0;0m  |   0.4691360487649683  |      +ve      |             \n",
      "  \u001b[1mrbf.lengthscale        \u001b[0;0m  |  0.23199112912844969  |      +ve      |  lnN(0.2, 1)\n",
      "  \u001b[1mGaussian_noise.variance\u001b[0;0m  |  0.16000000000000003  |   +ve fixed   |             \n"
     ]
    }
   ],
   "source": [
    "gpm.optimize_restarts(messages=True)\n",
    "print(gpm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "m_star, v_star = gpm.predict(x_star)\n",
    "f_lower = m_star - 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "f_upper = m_star + 2.0 * np.sqrt(v_star - gpm.likelihood.variance)\n",
    "y_lower = m_star - 2.0 * np.sqrt(v_star)\n",
    "y_upper = m_star + 2.0 * np.sqrt(v_star)\n",
    "ax.fill_between(x_star.flatten(), y_lower.flatten(), y_upper.flatten(), color='red', alpha=0.25, label='$y^*$ 95% pred.')\n",
    "ax.fill_between(x_star.flatten(), f_lower.flatten(), f_upper.flatten(), alpha=0.5, label='$f(\\mathbf{x}^*)$ 95% pred.')\n",
    "ax.plot(x_star, m_star, lw=2, label='$m_n(x)$')\n",
    "ax.plot(x_star, f_true(x_star), 'm-.', label='True function')\n",
    "ax.plot(X, Y, 'kx', markersize=10, markeredgewidth=2, label='data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's better, but not perfect.\n",
    "But remember: You don't know what the truth is..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions\n",
    "\n",
    "Let's investigate what happens to the previous examples as you increase the number of observations.\n",
    "\n",
    "+ Rerun everything gradually increasing the number of samples from $n=10$ to $n=100$.\n",
    "Notice that as the number of samples increases it doesn't really matter what your prior knowledge is.\n",
    "As a matter of fact, for the largest number of samples you try, pick a very wrong prior probability for $\\ell$.\n",
    "See what happens.\n",
    "\n",
    "+ Rerun everything with $\\sigma=0.01$ (small noise) and gradually increasing the number of samples from $n=10$ to $n=100$.\n",
    "For small noise, the model is trying to interpolate.\n",
    "Is it capable of figuring out that the noise is small when the number of observations is limited? When does the method realize the noise is indeed small?"
   ]
  }
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